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 A242391 Number of compositions of n in which each part has odd multiplicity. 3
 1, 1, 1, 4, 3, 10, 16, 28, 49, 91, 186, 266, 670, 884, 2350, 3028, 8259, 10536, 30241, 37382, 108628, 135550, 391202, 503750, 1429838, 1884659, 5222976, 7107138, 19119324, 27088726, 70366026, 103884570, 259884905, 399686188, 962312254, 1543116240, 3576132805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 EXAMPLE a(0) = 1: the empty composition. a(1) = 1: [1]. a(2) = 1: [2]. a(3) = 4: [3], [2,1], [1,2], [1,1,1]. a(4) = 3: [4], [3,1], [1,3]. a(5) = 10: [5], [4,1], [1,4], [3,2], [2,3], [2,1,1,1], [1,2,1,1], [1,1,2,1], [1,1,1,2], [1,1,1,1,1]. MAPLE b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(`if`(j=0 or irem(j, 2)=1, b(n-i*j, i-1, p+j)/j!, 0), j=0..n/i))) end: a:= n-> b(n\$2, 0): seq(a(n), n=0..45); MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, Sum[If[j==0 || Mod[j, 2]==1, b[n-i*j, i-1, p+j]/j!, 0], {j, 0, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 45}] (* Jean-François Alcover, Feb 08 2017, translated from Maple *) CROSSREFS Cf. A130495 (for even multiplicity). Sequence in context: A065763 A185730 A205965 * A241862 A222510 A100492 Adjacent sequences: A242388 A242389 A242390 * A242392 A242393 A242394 KEYWORD nonn AUTHOR Alois P. Heinz, May 12 2014 STATUS approved

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Last modified July 21 09:38 EDT 2024. Contains 374472 sequences. (Running on oeis4.)