The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238742 Number of partitions p of 2n+1 such that n - (number of parts of p) is a part of p. 3
 0, 0, 1, 5, 13, 31, 59, 109, 180, 301, 461, 712, 1051, 1547, 2200, 3138, 4349, 6036, 8211, 11146, 14901, 19908, 26232, 34513, 44953, 58412, 75244, 96752, 123448, 157201, 198931, 251155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Giovanni Resta, Table of n, a(n) for n = 1..1000 EXAMPLE a(4) counts these partitions of 9: 72, 711, 621, 531, 441. MATHEMATICA 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 12 2014 *) CROSSREFS Cf. A238640, A238741. Sequence in context: A332368 A203246 A106985 * A023261 A165888 A021007 Adjacent sequences: A238739 A238740 A238741 * A238743 A238744 A238745 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 04 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 15:05 EDT 2024. Contains 372826 sequences. (Running on oeis4.)