A293367 Number of partitions of n where each part i is marked with a word of length i over a ternary alphabet whose letters appear in alphabetical order and all three letters occur at least once in the partition.

10, 81, 396, 1751, 6528, 23892, 80979, 272085, 876342, 2821217, 8840964, 27713589, 85532512, 263935014, 806417553, 2464692788, 7483544643, 22727335830, 68734242687, 207887123472, 627024671262, 1891376241178, 5694616254570, 17146333061406, 51564199968339

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Formula

a(n) ~ c * 3^n, where c = 6.846206073498521357898163368676070142316815386135993166380819930419737... - 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))(3):
seq(a(n), n=3..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 = 3}, Sum[b[n, n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]];
a /@ Range[3, 30] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)

Crossrefs

Column k=3 of A261719.

Cf. A261737.

Sequence in context: A138425 A010569 A136870 * A018202 A154236 A095004

Adjacent sequences: A293364 A293365 A293366 * A293368 A293369 A293370

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2017

Status

approved