A026924 Number of partitions of n into an odd number of parts, the greatest being 4; also, a(n+7) = number of partitions of n+3 into an even number of parts, each <=4.

0, 0, 0, 1, 0, 1, 1, 3, 3, 5, 5, 8, 8, 12, 13, 18, 19, 24, 26, 33, 35, 43, 46, 55, 59, 69, 74, 86, 91, 104, 111, 126, 134, 150, 159, 177, 187, 207, 219, 241, 254, 277, 292, 318, 334, 362, 380, 410, 430, 462, 484, 519, 542, 579, 605

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..394

Crossrefs

4th column of A026920.

Programs

Maple

A026924 := proc(n)
    local a,p1,p2,p3,p4 ;
    a := 0 ;
    for p1 from 0 to n do
        for p2 from 0 to (n-p1)/2 do
            for p3 from op(1+modp(n-p1-2*p2,4),[0,3,2,1]) to (n-p1-2*p2)/3 by 4 do
                p4 := (n-p1-2*p2-3*p3)/4 ;
                if type(p4,'integer') and p4 >=1 and type(p1+p2+p3+p4,'odd') then
                    a := a+1 ;
                end if:
            end do:
        end do:
    end do:
    a;
end proc: # R. J. Mathar, Aug 22 2019

Formula

a(n) + A026928(n) = A026810(n). - R. J. Mathar, Aug 22 2019