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A092269
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Spt function: total number of smallest parts in all partitions of n.
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22
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1, 3, 5, 10, 14, 26, 35, 57, 80, 119, 161, 238, 315, 440, 589, 801, 1048, 1407, 1820, 2399, 3087, 3998, 5092, 6545, 8263, 10486, 13165, 16562, 20630, 25773, 31897, 39546, 48692, 59960, 73423, 89937, 109553, 133439, 161840, 196168, 236843
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| F. Garvan, Table of a(n) for n=1..10000 Coefficients of Andrews spt-function
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
G. E. Andrews, F. G. Garvan, and J. Liang, Self-conjugate vector partitions and the parity of the spt-function
A. Folsom and K. Ono, The spt-function of Andrews
F. G. Garvan, Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences
F. G. Garvan, Congruences for Andrews' spt-function modulo powers of 5, 7 and 13
K. Ono, Congruences for the Andrews spt-function
Wikipedia, Spt function
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FORMULA
| G.f.: Sum(x^n/(1-x^n)*Product(1/(1-x^k), k = n .. infinity), n = 1 .. infinity).
a(n) = A000070(n-1) + A195820(n). - Omar E. Pol, Oct 19 2011
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EXAMPLE
| Partitions of 4 are [1,1,1,1], [1,1,2], [2,2], [1,3], [4]. 1 appears 4 times in the first, 1 twice in the second, 2 twice n the third, etc.; thus a(4)=4+2+2+1+1=10.
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CROSSREFS
| Cf. A092314, A092322, A092309, A092321, A092313, A092310, A092311, A092268, A006128.
Cf. A195053. - Omar E. Pol, Jan 14 2012
Sequence in context: A008610 A078411 A137630 * A182722 A089483 A190484
Adjacent sequences: A092266 A092267 A092268 * A092270 A092271 A092272
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 16 2004
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EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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