President Reagan is considering a new kind of math under which he might be able to increase defense spending as much as promised over the long run and still balance the budget by 1984.

Pentagon officials said yesterday he is contemplating raising the defense budget less than proposed for the next three years, but promising to increase it more than proposed in 1985 and thereafter.

Defense Secretary Caspar W. Weinberger intends to fight this suggested sliding scale when he meets with Reagan at the White House today to discuss how much is enough for defense, Pentagon officials said.

The Weinberger line will be that the Soviet military buildup requires the full increase in the U.S. defense budget that the administration promised Congress shortly after taking office--7 percent per year after allowing for inflation.

Weinberger also wants to make the fiscal 1982 defense budget, as revised by Reagan, the starting point for these "real" increases. Budget-cutters in the administration want to use the much lower 1981 budget instead; it would be a much easier starting point.

There is one other footnote to the debate: the increases under study would not be in actual spending for the years in question, but in so-called obligational authority or the right to spend in future years.

Partly to make sure the extra money is spent in an orderly fashion, Weinberger thinks the increases should come at a fairly steady pace, 7 percent or close to it in every year.

But some White House officials are urging the president to settle for much smaller growth in the fiscal 1983 and 1984 defense budgets to make it easier to balance the 1984 budget. Otherwise, they warn, Reagan will have to make such deep cuts in domestic programs that Congress may refuse to go along, breaking the president's spell over the legislative branch in the process.

"Some of the options under consideration would slow growth dramatically" in the defense budget, one administration executive said. Instead of 7 percent real growth, the Pentagon 1982 budget would be increased in 1983 by only enough to make up for inflation under one of the more drastic proposals.

However, to take the political sting out of such slow growth in defense now, the administration would promise to make up for it in 1985 and 1986 with increases of much more than 7 percent. One problem with this scheme is that Reagan faces a reelection contest in 1984.

This idea, while helpful in the effort to balance the federal budget by 1984, would jeopardize Weinberger's pledge to get the most bang for the taxpayer's buck. He has said repeatedly that a feast-and-famine approach wastes money and sows confusion in the defense industry.

Also, if Reagan ends up saying that it is safe to slow his rearmament effort for a year or two, he risks breaking up the pro-defense coalition in Congress.

The coalition went along with his requests to increase the defense budget from $178 billion to $222.2 billion in obligational authority and from $158.6 billion to $184.8 billion in outlays between fiscal 198l and 1982. Those increases come to 24 and 16 percent respectively before inflation.

Under Reagan's five-year defense plan for fiscal 1982 through fiscal 1986, as announced by the Pentagon in March, these real, after-inflation increases in total obligational authority were promised: fiscal 1982, 14.6 percent; 1983, 7.3 percent; 1984, 7 percent; 1985, 7 percent; 1986, 7 percent.

The administration started backing away from those projected increases when a White House spokesman told reporters in Santa Barbara, Calif., on Aug. 25 that the 7 percent annual increase "was a cap," not a firm commitment.

Pentagon officials are saying both in private and in public that anything less than 7 percent per year real increases will require cuts all across the board in defense programs, including in research and production contracts carefully guarded by lawmakers from states in which such work is done.

Counter-arguments by Budget Director David A. Stockman and others in his camp are that it is high time that the Pentagon share in the cuts needed to balance the federal budget.

Such cuts, they contend, will help preserve the congressional constituency for tax and domestic spending cuts; convince the investment community that the administration is determined to bring federal spending under control, and go a long way toward balancing the government's budget.