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 A238629 Number of partitions p of n such that n - 2*(number of parts of p) is a part of p. 1
 0, 0, 0, 0, 1, 1, 4, 4, 9, 9, 18, 18, 31, 31, 51, 51, 79, 79, 119, 119, 173, 173, 248, 248, 347, 347, 480, 480, 654, 654, 883, 883, 1178, 1178, 1561, 1561, 2049, 2049, 2674, 2674, 3464, 3464, 4464, 4464, 5717, 5717, 7290, 7290, 9246, 9246, 11680, 11680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 LINKS Giovanni Resta, Table of n, a(n) for n = 1..1000 EXAMPLE a(7) counts these partitions: 511, 43, 421, 331. MATHEMATICA Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, n - 2*Length[p]]], {n, 50}] 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_] := a[n] = Sum[q[n, u, n - 2*u], {u, (n - 1)/2}]; Array[a, 100] (* Giovanni Resta, Mar 09 2014 *) CROSSREFS Cf. A000027 = (number of partitions p of n such that n - (number of parts of p) is a part of p) = n-2 for n >=3. Sequence in context: A008794 A075709 A332777 * A192032 A116682 A168157 Adjacent sequences: A238626 A238627 A238628 * A238630 A238631 A238632 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 02 2014 STATUS approved

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Last modified August 7 17:47 EDT 2024. Contains 375017 sequences. (Running on oeis4.)