A391705 Number of plane partitions of n with 6 parts.

11, 11, 31, 54, 99, 150, 246, 349, 525, 725, 1014, 1349, 1821, 2348, 3058, 3869, 4899, 6070, 7539, 9179, 11197, 13453, 16152, 19167, 22738, 26678, 31290, 36382, 42250, 48703, 56091, 64156, 73321, 83314, 94549, 106770, 120444, 135234, 151697, 169480, 189132, 210307

Offset

6,1

Links

Table of n, a(n) for n=6..47.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,0,0,1,0,2,0,-1,-1,-1,-1,0,2,0,1,0,0,-1,-1,1).

Formula

G.f.: (q^17 + q^15 + 6*q^14 + 6*q^13 + 8*q^12 + 8*q^11 + 14*q^10 + 12*q^9 + 9*q^8 + 11*q^6)/(Product_{k=1..6} (1 - q^k)).

Prog

(PARI) A_q(N) = {my(q='q+O('q^(N))); Vec((q^17 + q^15 + 6*q^14 + 6*q^13 + 8*q^12 + 8*q^11 + 14*q^10 + 12*q^9 + 9*q^8 + 11*q^6)/prod(k=1, 6, 1-q^k))}

Crossrefs

Column k=6 of A091298.

Cf. A000219, A392995.

Sequence in context: A218163 A152082 A070849 * A124297 A172507 A089766

Adjacent sequences: A391702 A391703 A391704 * A391706 A391707 A391708

Keyword

nonn,easy

Author

John Tyler Rascoe, Feb 26 2026

Status

approved