A220505 a(n) = spt(5n+4)/5 where spt(n) = A092269(n).

2, 16, 88, 364, 1309, 4126, 11992, 32368, 82590, 200487, 467152, 1049224, 2283364, 4829302, 9959035, 20069790, 39612612, 76703340, 145945332, 273224940, 503888206, 916373028, 1644925432, 2916814954, 5113148026, 8866911378, 15220453704

Offset

0,1

Comments

That spt(5n+4) == 0 (mod 5) is one of the congruences stated by George E. Andrews. See theorem 2 in the Andrews' paper. See also A220507 and A220513.

Links

Table of n, a(n) for n=0..26.

G. E. Andrews, The number of smallest parts in the partitions of n

G. E. Andrews, F. G. Garvan, and J. Liang, Combinatorial interpretation of congruences for the spt-function

K. C. Garrett, C. McEachern, T. Frederick, O. Hall-Holt, Fast computation of Andrews' smallest part statistic and conjectured congruences, Discrete Applied Mathematics, 159 (2011), 1377-1380.

F. G. Garvan, Congruences for Andrews' smallest parts partition function and new congruences for Dyson's rank

F. G. Garvan, Congruences for Andrews' spt-function modulo powers of 5, 7 and 13

F. G. Garvan, Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences, arXiv:1011.1957 [math.NT], 2010.

K. Ono, Congruences for the Andrews spt-function

Formula

a(n) = A092269(A016897(n))/5 = A220485(n)/5.

Mathematica

b[n_, i_] := b[n, i] = If[n==0 || i==1, n, {q, r} = QuotientRemainder[n, i]; If[r == 0, q, 0] + Sum[b[n - i j, i - 1], {j, 0, n/i}]];
spt[n_] := b[n, n];
a[n_] := spt[5n+4]/5;
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Jan 30 2019, after Alois P. Heinz in A092269 *)

Crossrefs

Cf. A016897, A071734, A092269, A220485, A220507, A220513.

Sequence in context: A207891 A207655 A071893 * A370192 A069440 A000431

Adjacent sequences: A220502 A220503 A220504 * A220506 A220507 A220508

Keyword

nonn

Author

Omar E. Pol, Jan 18 2013

Status

approved