A261738 Number of partitions of n where each part i is marked with a word of length i over a quaternary alphabet whose letters appear in alphabetical order.

1, 4, 26, 124, 631, 2780, 12954, 55196, 241634, 1012196, 4280046, 17636252, 73157709, 298342936, 1220952044, 4947485904, 20079338277, 80987461760, 326986050564, 1314939934216, 5290893771329, 21236552526364, 85263892578686, 341801704446572, 1370448001291679

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ c * 4^n, where c = Product_{k>=2} 1/(1 - (k+1)*(k+2)*(k+3)/(3*2^(2*k+1))) = 4.90673361196637084263021203165784685586076564592828337755053385514766785... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+3,3)*x^k). - Ilya Gutkovskiy, May 09 2021

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+3, 3))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, b[n - i, i] Binomial[i + 3, 3]]]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A261718.

Sequence in context: A267847 A211166 A245460 * A363648 A184263 A058408

Adjacent sequences: A261735 A261736 A261737 * A261739 A261740 A261741

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved