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A220513
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a(n) = spt(13n+6)/13 where spt(n) = A092269(n).
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3
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2, 140, 3042, 38054, 344212, 2488260, 15235620, 81926240, 396603536, 1759312286, 7246532360, 27998586490, 102294344881, 355704104008, 1183463874068, 3784162891544, 11672177600660, 34840196162760, 100912078549712, 284295561826160
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..19.
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
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FORMULA
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a(n) = A092269(A186113(n))/13 = A220503(n)/13.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A076394, A092269, A186113, A220503, A220505, A220507.
Sequence in context: A093887 A152005 A140898 * A120814 A221601 A334013
Adjacent sequences: A220510 A220511 A220512 * A220514 A220515 A220516
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol, Jan 18 2013
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STATUS
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approved
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