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A221141 Third-order spt function. 3
0, 0, 1, 7, 28, 85, 217, 497, 1036, 2044, 3787, 6797, 11648, 19558, 31703, 50645, 78674, 120932, 181664, 270600, 395682, 574329, 820834, 1166109, 1634668, 2279242, 3142903, 4312063, 5859616, 7927745, 10635129, 14209328, 18846744, 24900807, 32688145, 42761047 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..50

F. G. Garvan, Higher-order spt functions, preprint.

F. G. Garvan, Higher-order spt functions, arXiv:1008.1207 [math.NT], 2010.

F. G. Garvan, Higher-order spt functions, Adv. Math. 228 (2011), no. 1, 241-265.

MATHEMATICA

om[3, p_List] := Module[{pu, m, f}, pu = Union[p]; m = Length[pu]; f[j_] := Count[p, pu[[j]]]; Binomial[f[1] + 2, 5] + Binomial[f[1] + 1, 3] Sum[ Binomial[f[j] + 1, 2], {j, 2, m}] + f[1] Sum[Binomial[f[j] + 2, 4], {j, 2, m}] + f[1] Sum[Binomial[f[j] + 1, 2] Binomial[f[k] + 1, 2], {j, 2, m}, {k, j + 1, m}]];

spt[3, n_] := Sum[om[3, p], {p, IntegerPartitions[n]}];

Table[spt[3, n], {n, 1, 29}] (* Jean-François Alcover, Mar 30 2020 *)

CROSSREFS

Cf. A092269, A221140, A221142, A221143, A221144.

Sequence in context: A243741 A145456 A145135 * A144900 A054469 A156928

Adjacent sequences:  A221138 A221139 A221140 * A221142 A221143 A221144

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 02 2013

EXTENSIONS

More terms from Jean-François Alcover, Mar 30 2020

STATUS

approved

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)