A389773 - OEIS

A389773

One third the number of solid partitions of n with 6 parts.

16, 16, 53, 99, 184, 291, 484, 717, 1092, 1540, 2180, 2957, 4022, 5271, 6914, 8847, 11278, 14113, 17618, 21637, 26515, 32073, 38679, 46175, 54969, 64840, 76300, 89113, 103803, 120135, 138718, 159245, 182434, 207948, 236526, 267862, 302766, 340844, 383048, 428946

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OFFSET

6,1

LINKS

Table of n, a(n) for n=6..45.

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.: (4*q^17 + 5*q^16 + 5*q^15 + 22*q^14 + 27*q^13 + 25*q^12 + 24*q^11 + 32*q^10 + 30*q^9 + 21*q^8 + 16*q^6)/(Product_{k=1..6} (1 - q^k)).

PROG

(PARI)

A_q(N) = {Vec((4*q^17 + 5*q^16 + 5*q^15 + 22*q^14 + 27*q^13 + 25*q^12 + 24*q^11 + 32*q^10 + 30*q^9 + 21*q^8 + 16*q^6)/prod(k=1, 6, 1-q^k) + O('q^(N+1)))}

CROSSREFS

3*a(n) is column k=6 of A380893.

Cf. A000219, A000293, A002836, A207542, A379277.

Sequence in context: A278348 A022350 A226068 * A230977 A393214 A382743

Adjacent sequences: A389770 A389771 A389772 * A389774 A389775 A389776

KEYWORD

nonn,easy

AUTHOR

John Tyler Rascoe, Oct 14 2025

STATUS

approved