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A240609 Number of n-length words w over a 3-ary alphabet such that w is empty or a prefix z concatenated with letter a_i and i=1 or 0 < #(z,a_{i-1}) >= #(z,a_i), where #(z,a_i) counts the occurrences of the i-th letter in z. 2
1, 1, 2, 5, 13, 35, 94, 254, 688, 1872, 5115, 14038, 38689, 107055, 297336, 828699, 2317098, 6498114, 18273861, 51521238, 145604868, 412407942, 1170507375, 3328570513, 9482518041, 27059673745, 77340925350, 221382318131, 634578781229, 1821388557507 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ 29 * 3^(n+3/2) / (16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jul 16 2014

EXAMPLE

a(3) = 5: 111, 112, 121, 122, 123.

a(4) = 13: 1111, 1112, 1121, 1122, 1123, 1211, 1212, 1213, 1221, 1223, 1231, 1232, 1233.

a(5) = 35: 11111, 11112, 11121, 11122, 11123, 11211, 11212, 11213, 11221, 11222, 11223, 11231, 11232, 11233, 12111, 12112, 12113, 12121, 12122, 12123, 12131, 12132, 12133, 12211, 12212, 12213, 12231, 12233, 12311, 12312, 12313, 12321, 12323, 12331, 12332.

MAPLE

a:= proc(n) option remember; `if`(n<3, [1, 1, 2][n+1],

      ((87*n^5-380*n^4-95*n^3+848*n^2-76*n+96) *a(n-1)

      +(n-1)*(29*n^4-117*n^3+228*n^2+404*n-528) *a(n-2)

      -3*(n-1)*(n-2)*(29*n^3-59*n^2-34*n-96) *a(n-3))/

      ((n-2)*(n+4)*(29*n^3-146*n^2+171*n-150)))

    end:

seq(a(n), n=0..35);

MATHEMATICA

b[n_, k_, l_] := b[n, k, l] = If[n == 0, 1, If[Length[l] < k, b[n - 1, k, Append[l, 1]], 0] + Sum[If[i == 1 || l[[i]] <= l[[i - 1]], b[n - 1, k, ReplacePart[l, i -> l[[i]] + 1]], 0], {i, 1, Length[l]}]];

a[n_] := b[n, Min[3, n], {}];

a /@ Range[0, 35] (* Jean-François Alcover, Jan 03 2021, after Alois P. Heinz in A240608 *)

CROSSREFS

Column k=3 of A240608.

Sequence in context: A097919 A160438 A335725 * A054657 A024576 A057960

Adjacent sequences:  A240606 A240607 A240608 * A240610 A240611 A240612

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 09 2014

STATUS

approved

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Last modified November 30 08:19 EST 2021. Contains 349419 sequences. (Running on oeis4.)