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 A220513 a(n) = spt(13n+6)/13 where spt(n) = A092269(n). 3
 2, 140, 3042, 38054, 344212, 2488260, 15235620, 81926240, 396603536, 1759312286, 7246532360, 27998586490, 102294344881, 355704104008, 1183463874068, 3784162891544, 11672177600660, 34840196162760, 100912078549712, 284295561826160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS That spt(13n+6) == 0 (mod 13) is one of the congruences stated by George E. Andrews. See theorem 2 in the Andrews' paper. See also A220505 and A220507. 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' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences, arXiv:1011.1957 [math.NT], 2010. FORMULA a(n) = A092269(A186113(n))/13 = A220503(n)/13. 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[13 n + 6]/13; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Jan 30 2019, after Alois P. Heinz in A092269 *) CROSSREFS Cf. A076394, A092269, A186113, A220503, A220505, A220507. Sequence in context: A093887 A152005 A140898 * A120814 A221601 A334013 Adjacent sequences: A220510 A220511 A220512 * A220514 A220515 A220516 KEYWORD nonn AUTHOR Omar E. Pol, Jan 18 2013 STATUS approved

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Last modified March 23 23:09 EDT 2023. Contains 361454 sequences. (Running on oeis4.)