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A238641
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Number of partitions p of 2n-1 such that n - (number of parts of p) is a part of p.
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3
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0, 0, 1, 4, 9, 21, 37, 69, 113, 187, 286, 449, 657, 976, 1397, 2003, 2788, 3902, 5323, 7284, 9789, 13144, 17405, 23052, 30142, 39379, 50967, 65842, 84368, 107954, 137126, 173893
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OFFSET
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1,4
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LINKS
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EXAMPLE
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a(4) counts these partitions of 7: 52, 511, 421, 331.
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MATHEMATICA
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z = 30; g[n_] := IntegerPartitions[n]; m[p_, t_] := MemberQ[p, t];
Table[Count[g[2 n], p_ /; m[p, n - Length[p]]], {n, z}] (*A238607*)
Table[Count[g[2 n - 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238641*)
Table[Count[g[2 n + 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238742*)
p[n_, k_] := p[n, k] = If[k == 1 || n == k, 1, If[k > n, 0, p[n - 1, k - 1] + p[n - k, k]]]; q[n_, k_, e_] := q[n, k, e] = If[n - e < k - 1 , 0, If[k == 1, If[n == e, 1, 0], p[n - e, k - 1]]]; a[n_] := Sum[q[2*n - 1, u, n - u], {u, n - 1}]; Array[a, 100] (* Giovanni Resta, Mar 09 2014 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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