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A182708
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a(n) is the sum of the smallest parts of all partitions of n that do not contain 1 as a part.
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4
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0, 2, 3, 6, 7, 13, 14, 23, 27, 39, 45, 67, 75, 104, 125, 165, 194, 258, 302, 392, 467, 588, 700, 885, 1045, 1296, 1546, 1897, 2249, 2753, 3252, 3945, 4670, 5616, 6633, 7957, 9357, 11157, 13124, 15573, 18257, 21599, 25259, 29760, 34760, 40788, 47526, 55642, 64669, 75465, 87576, 101898, 117991, 136977, 158286
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OFFSET
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1,2
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COMMENTS
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In other words, sum of the smallest parts of all partitions of the head of the last section of the set of partitions of n.
Only one of the smallest parts is used in the sum.
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A046746(n) - A000041(n-1).
a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (6*sqrt(2)*n^(3/2)) * (1 + (11*Pi/(24*sqrt(6)) - 3*sqrt(3/2)/Pi)/sqrt(n)). - Vaclav Kotesovec, Jan 03 2019, extended Jul 06 2019
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MATHEMATICA
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Table[Total[{Min /@ IntegerPartitions[n, All, Range[2, n]]}, 2], {n, 55}] (* Robert Price, Aug 30 2020 *) (* Only suitable for n<100 *)
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PROG
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(PARI) my(N=66, z='z+O('z^N)); gf=sum(k=1, N, k * z^k / prod(j=k, N, 1-z^j ) ) - z/eta(z); concat([0], Vec(gf)) \\ Joerg Arndt, Aug 31 2020
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CROSSREFS
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Cf. A000041, A046746, A135010, A138121, A182707, A182709.
Sequence in context: A255940 A167415 A018511 * A304709 A330145 A183558
Adjacent sequences: A182705 A182706 A182707 * A182709 A182710 A182711
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KEYWORD
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nonn,easy
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AUTHOR
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Omar E. Pol, Nov 28 2010
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STATUS
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approved
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