Over cries of protest and continuing court challenges from Frost Belt cities, the U.S. Census Bureau officially announced its final 1980 population count yesterday. The figures confirm a massive population shift to the West and South which carries with it millions in federal funds and increased political power, including a change of 17 seats in the House of Representatives.

The census counted 226,504,825 Americans. Unless altered by court cases pending in 13 states, that number will become the basis for reapportionment of the 435-seat House in time for the November 1982 elections. Florida is the top gainer, adding four seats for a total of 19. New York lost five seats, for a new total of 34.

In all, 11 states gained seats, while 10 lost. Texas is the second biggest winner, picking up three seats, for a total of 27. California, the most populous state, is next with a gain of two seats, for the largest single total -- 45.

Illinois, Ohio and Pennsylvania each lost two seats. Maryland and Virginia are unchanged.

The new count shows a national population increase of 11.4 percent since 1970. Although the demographic patterns shifted, only New York, Rhode Island and the District of Columbia actually lost population, based on preliminary breakdowns, officials said. All 48 other states gained, though to wildly varying degrees.

Nevada, for example, underwent a population explosion of 63.3 percent, giving it a total of 797,899 people -- still a relatively thin crowd. Massachusetts gained only 0.6 percent, but that small state still hosts over 5.7 million individuals.

The breakdown by region is dramatic while the industrial Northeast lost 0.2 percent, and the north central states lost 3.6 percent, the West picked up 23.2 percent and the South gained 19 percent.

Since the 1970 headcount, the South and West have overtaken and passed the Northeast and north central regions in population. The new count shows roughly 117.7 million people in the former, about 108 million in the latter.

As reported earlier, the District has lost 16.1 percent of its population, dropping to 635,185, based on preliminary figures. At the same time, the Washington metropolitan area posulation overall grew by 4.5 percent, with most of the growth in Northern Virginia suburbs, which showed a 19.7 percent increase. Although Maryland's Prince George's County also lost people (about 0.6 percent) it is now the most populous jurisdiction in the area, with 657,707 residents.

A final breakdown of figures for cities and other small jurisdictions will not be issued for about two months, officials said.

The Census Bureau was required by law to submit its figures to President Carter by the end of 1980. But a court challenge in New York threatened to hold up the process and federal officials sought an eleventh-hour assist from the Supreme Court. Late Tuesday, in a 7-to-1 vote, the high court removed the obstacle, at least long enough for the legal deadline to be met.

Numberous state and local officials have charged that the census short-changed their constituents by failing to count everybody, especially blacks and other minorities concentrated in large cities.

The battle over the census is a murky one, with disagreements to be worked out over definitions -- how to count illegal aliens, for instance -- and methods. At stake along with political power is the allocation of a substantial portion of the $90 billion in federal grants to cities and states every year.

The General Accounting Office released a report Tuesday on the Census Bureau's operations in a sample of 10 cities that contains some evidence of possible undercounting. The congressional watchdog agency reported, among ither discrepancies, "significant differences" in two cities -- New York and Pittsburgh -- comparing the tallies taken by census workers in person with those obtained through mail surveys as to the size of households.

New York contended in its suit that the census count of city residents was at least 800,000 low, with an additional 200,000 residents uncounted in the rest of the state.One reason for this, New York charged, was that census-takers were afraid to go into some poor neighborhoods.

Criss-checks to verify the count could have indefinitely delayed the reapportionment of the House of Representatives, government officials argued.

Vincent P. Barabba, director of the Census Bureau, yesterday described the 1980 census as "by far the most accurate census ever taken, a census that comes as close as possible to reflecting the actual number of citizens in this country."

But he noted that, as statistical specialists improve their methods, the official count will be adjusted to refelcet new findings as a basis for the distribution of federal funds.

He acknowledged also that the impending court decisions might force "widespread adjustnents." Those cases are in Colorado, Florida, Georgia, Illinois, Massachusetts, Michigan, Minnesota, Missouri, New Jersey, New Mexico, New York, North Carolina and Pennsylvania.