A258459 Number of partitions of n into parts of exactly 4 sorts which are introduced in ascending order.

1, 11, 77, 438, 2216, 10422, 46731, 202814, 860586, 3593561, 14834956, 60735095, 247155292, 1001318246, 4043482110, 16288762319, 65500024027, 263035832734, 1055252430510, 4230340216034, 16949359882259, 67881449170593, 271777855641517, 1087867649157513

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Formula

a(n) ~ c * 4^n, where c = 1/(24*Product_{n>=1} (1-1/4^n)) = 1/(24*QPochhammer[1/4, 1/4]) = 1/(24*A100221) = 0.060514735102066542326446... . - Vaclav Kotesovec, Jun 01 2015

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
    end:
T:= (n, k)-> add(b(n$2, k-i)*(-1)^i/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 4):
seq(a(n), n=4..35);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, k*b[n - i, i, k]]]];
T[n_, k_] := Sum[b[n, n, k - i]*(-1)^i/(i!*(k - i)!), {i, 0, k}];
Table[T[n, 4], {n, 4, 35}] (* Jean-François Alcover, May 25 2018, translated from Maple *)

Crossrefs

Column k=4 of A256130.

Cf. A320546.

Sequence in context: A355053 A023010 A303103 * A320547 A022639 A000589

Adjacent sequences: A258456 A258457 A258458 * A258460 A258461 A258462

Keyword

nonn

Author

Alois P. Heinz, May 30 2015

Status

approved