A226882 Number of n-length words w over ternary alphabet {a,b,c} such that #(w,a) >= #(w,b) >= #(w,c) >= 1, where #(w,x) counts the letters x in word w.

6, 12, 50, 180, 497, 1484, 5154, 13680, 41327, 134508, 368095, 1095367, 3521156, 9733564, 29025290, 92208816, 257946527, 769203752, 2428043309, 6848294497, 20442949562, 64191187508, 182286409175, 544512163065, 1702858693902, 4861764643419, 14531465607434

Offset

3,1

Links

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

Vaclav Kotesovec, Recurrence (of order 9)

Formula

a(n) ~ 3^n/6 * (1 + 3*sqrt(3/(Pi*n))/2+sqrt(3)*(1+2*cos(2*Pi*n/3))/(Pi*n)). - Vaclav Kotesovec, Aug 29 2014

Example

a(4) = 12: aabc, aacb, abac, abca, acab, acba, baac, baca, bcaa, caab, caba, cbaa.

Mathematica

Table[Sum[n!/Product[IntegerPartitions[n, {3}][[k, j]]!, {j, 1, 3}], {k, 1, Length[IntegerPartitions[n, {3}]]}], {n, 3, 30}] (* Vaclav Kotesovec, Aug 29 2014 *)

Crossrefs

Column k=3 of A226874.

Sequence in context: A032470 A342302 A018809 * A214903 A372900 A256584

Adjacent sequences: A226879 A226880 A226881 * A226883 A226884 A226885

Keyword

nonn

Author

Alois P. Heinz, Jun 21 2013

Status

approved