A389773 - OEIS

%I #7 Oct 26 2025 18:04:27

%S 16,16,53,99,184,291,484,717,1092,1540,2180,2957,4022,5271,6914,8847,

%T 11278,14113,17618,21637,26515,32073,38679,46175,54969,64840,76300,

%U 89113,103803,120135,138718,159245,182434,207948,236526,267862,302766,340844,383048,428946

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

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1).

%F 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)).

%o (PARI)

%o 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)))}

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

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

%K nonn,easy

%O 6,1

%A _John Tyler Rascoe_, Oct 14 2025