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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified May 21 16:41 EDT 2024. Contains 372738 sequences. (Running on oeis4.)