A293368 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 and all four letters occur at least once in the partition.

47, 544, 4232, 25100, 136516, 666800, 3142884, 14024256, 61637303, 262474700, 1109010890, 4603058016, 19018730793, 77751623552, 317106002688, 1284961711836, 5199893190893, 20961427995916, 84431958561230, 339292817869492, 1362880886322817, 5466605564267372

Offset

4,1

Links

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

Formula

a(n) ~ c * 4^n, where c = 4.90673361196637084263021203165784685586076564592828337755053385514766785... - Vaclav Kotesovec, Oct 11 2017

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, b(n-i, i, k)*binomial(i+k-1, k-1))))
    end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(4):
seq(a(n), n=4..30);

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, b[n - i, i, k] Binomial[i + k - 1, k - 1]]]];
a[n_] := With[{k = 4}, Sum[b[n, n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]];
a /@ Range[4, 30] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A261719.

Sequence in context: A009086 A034779 A201090 * A116146 A142253 A142577

Adjacent sequences: A293365 A293366 A293367 * A293369 A293370 A293371

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2017

Status

approved