A227552 Number of partitions of n into distinct parts with maximal boundary size.
1, 1, 1, 1, 1, 2, 3, 1, 2, 2, 4, 6, 1, 1, 3, 4, 6, 9, 14, 1, 2, 3, 5, 8, 11, 17, 24, 1, 1, 3, 5, 8, 11, 18, 24, 35, 49, 1, 2, 3, 6, 9, 14, 21, 30, 42, 60, 81, 1, 1, 3, 5, 9, 13, 21, 29, 43, 60, 84, 113, 156, 1, 2, 3, 6, 10, 15, 24, 35, 50, 71, 99, 134, 184, 246
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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Maple
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t>1, x, 1), expand(`if`(i<1, 0, `if`(t>1, x, 1)*b(n, i-1, iquo(t, 2))+ `if`(i>n, 0, `if`(t=2, x, 1)*b(n-i, i-1, iquo(t, 2)+2))))) end: a:= n-> (p->coeff(p, x, degree(p)))(b(n$2, 0)): seq(a(n), n=0..100);
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Mathematica
b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t>1, x, 1], Expand[If[i<1, 0, If[t>1, x, 1]*b[n, i-1, Quotient[t, 2]] + If[i>n, 0, If[t==2, x, 1] * b[n-i, i-1, Quotient[t, 2]+2]]]]]; a[n_] := Function [p, Coefficient[p, x, Exponent[p, x]]][b[n, n, 0]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)
Comments