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A238607
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Number of partitions p of 2n 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, 12, 24, 49, 85, 147, 232, 374, 558, 843, 1223, 1774, 2493, 3519, 4835, 6659, 8999, 12144, 16152, 21479, 28186, 36945, 47959, 62126, 79805, 102352, 130286, 165546, 209070, 263461, 330266, 413207, 514486, 639342, 791261, 977301, 1202636, 1477172
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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 8: 62, 611, 521, 431.
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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_] := 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, u, n-u], {u, n-1}]; Array[a, 100] (* Giovanni Resta, Mar 07 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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EXTENSIONS
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STATUS
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approved
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