A213873 Number of words w where each letter of the ternary alphabet occurs n times and for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.

1, 6, 15, 106, 1075, 13326, 188196, 2914395, 48349015, 846167608, 15456538890, 292407484590, 5695907466120, 113735416237808, 2319861446805120, 48199341935153655, 1017747539683821855, 21799192392184931700, 472889100118180757550, 10375788309377599231200

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..706

Formula

a(n) ~ 797*sqrt(3)*27^(n-1)/(16*Pi*n^4). - Vaclav Kotesovec, Aug 13 2013

For n > 1, a(n) = 3*(-4 + 108*n - 397*n^2 - 72*n^3 + 797*n^4) * (3*n-4)! / (2*(2*n-1)*(2*n+1) * (n-2)! * (n+1)! * (n+2)!). - Vaclav Kotesovec, Sep 02 2014

Example

a(0) = 1: the empty word.
a(1) = 6: abc, acb, bac, bca, cab, cba, (all permutations of 3 letters).
a(2) = 15: aabbcc, aabcbc, aacbbc, ababcc, abacbc, abcabc, acabbc, acbabc, baabcc, baacbc, bacabc, bcaabc, caabbc, cababc, cbaabc.

Maple

a:= proc(n) option remember; `if`(n<2, [1, 6][n+1], (6*n-9) *(3*n-4)
      *(3*n-5) *(797*n^4-72*n^3-397*n^2+108*n-4) *a(n-1) / ((n+1)
      *(n+2) *(2*n+1) *(797*n^4-3260*n^3+4601*n^2-2502*n+360)))
    end:
seq(a(n), n=0..20);

Mathematica

Flatten[{1, 6, Table[3*(-4 + 108*n - 397*n^2 - 72*n^3 + 797*n^4) * (3*n-4)! / (2*(2*n-1)*(2*n+1) * (n-2)! * (n+1)! * (n+2)!), {n, 2, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

Crossrefs

Column k=3 of A213275.

Sequence in context: A013222 A013228 A133472 * A219771 A087137 A056317

Adjacent sequences: A213870 A213871 A213872 * A213874 A213875 A213876

Keyword

nonn

Author

Alois P. Heinz, Jun 23 2012

Status

approved