A220507 a(n) = spt(7n+5)/7 where spt(n) = A092269(n).

2, 34, 260, 1498, 6956, 28024, 100953, 333680, 1026540, 2976024, 8197962, 21608760, 54788100, 134217717, 318816426, 736549424, 1659169712, 3652248590, 7870890952, 16633964444, 34522173765, 70450341042, 141526909340, 280158178412

Offset: 0

Author

Omar E. Pol, Jan 18 2013

Keywords

• nonn

Comments

That spt(7n+5) == 0 (mod 7) is one of the congruences stated by George E. Andrews. See theorem 2 in the Andrews' paper. See also A220505 and A220513.

Links

• 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

Crossrefs

Cf. A017041, A071746, A092269, A220502, A220505, A220513.

Programs

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[7 n + 5]/7;
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jan 30 2019, after Alois P. Heinz in A092269 *)

Formula

a(n) = A092269(A017041(n))/7 = A220502(n)/7.