A213288 Number of 9-length words w over n-ary alphabet such that 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.
0, 1, 162, 2074, 13280, 64924, 273248, 1050777, 3754472, 12602451, 39598078, 115470300, 311272072, 777274550, 1808153452, 3946185587, 8137258032, 15957939797, 29935676058, 53988338158, 94013898576, 158665898944, 260355640952, 416527654621, 651260985944
Offset: 0
Examples
a(0) = 0: no word of length 9 is possible for an empty alphabet.
a(1) = 1: aaaaaaaaa for alphabet {a}.
a(2) = 162: aaaaaaaaa, aaaaaaaab, ..., baabababa, bbbbbbbbb for alphabet {a,b}.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Crossrefs
Row n=9 of A213276.
Programs
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Maple
a:= n-> n*(3353416+ (-9177198+ (10002755+ (-5796570+ (1984509+ (-416052+ (52920+ (-3780+120*n) *n) *n) *n) *n) *n) *n) *n)/120: seq(a(n), n=0..40);
Formula
a(n) = n*(3353416 -9177198*n +10002755*n^2 -5796570*n^3 +1984509*n^4 -416052*n^5 +52920*n^6 -3780*n^7 +120*n^8)/120.
G.f.: x*(1+152*x +499*x^2 -290*x^3 +6224*x^4 +6496*x^5 +41203*x^6 +52034*x^7 +256561*x^8) / (1-x)^10.