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A097091 Number of partitions of n such that the least part occurs exactly three times. 5
0, 0, 1, 0, 1, 2, 2, 2, 6, 5, 8, 11, 15, 18, 27, 30, 43, 54, 69, 83, 113, 134, 172, 211, 265, 320, 405, 483, 602, 726, 888, 1064, 1306, 1554, 1884, 2248, 2707, 3213, 3860, 4560, 5446, 6435, 7638, 8990, 10651, 12494, 14734, 17260, 20277, 23683, 27754, 32328 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Number of partitions p of n such that 2*min(p) + (number of parts of p) is a part of p. - Clark Kimberling, Feb 28 2014

LINKS

Table of n, a(n) for n=1..52.

FORMULA

G.f.: Sum_{m>0} (x^(3*m) / Product_{i>m} (1-x^i)). More generally, g.f. for number of partitions of n such that the least part occurs exactly k times is Sum_{m>0} (x^(k*m) / Product_{i>m} (1-x^i)). Vladeta Jovovic

MATHEMATICA

a[n_] := Module[{p = IntegerPartitions[n], l = PartitionsP[n], c = 0, k = 1}, While[k < l + 1, q = PadLeft[p[[k]], 4]; If[q[[1]] != q[[4]] && q[[2]] == q[[4]], c++]; k++]; c]; Table[ a[n], {n, 52}]

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Length[p] + 2*Min[p]]], {n, 50}] (* Clark Kimberling, Feb 28 2014 *)

CROSSREFS

Cf. A002865, A096373, A097093, A097093.

Sequence in context: A210740 A209820 A145890 * A094204 A088681 A078584

Adjacent sequences:  A097088 A097089 A097090 * A097092 A097093 A097094

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jul 24 2004

STATUS

approved

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Last modified October 16 03:34 EDT 2019. Contains 328040 sequences. (Running on oeis4.)