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<a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (7, 12, 34, 59, 109, 166, 258, 352, 483, 606, 754, 875, 1007, 1087, 1161, 1172, 1167, 1099, 1023, 895, 775, 628, 503, 371, 273, 179, 118, 66, 38, 15, 8).

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nonn,easy

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Column k=9 of A242464.

G.f.: -(x+1) *(x^4-x^3+x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^2+x+1) *(x^6+x^3+1) *(x^2+1)*(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2-x+1) / (8*x^31 +15*x^30 +38*x^29 +66*x^28 +118*x^27 +179*x^26 +273*x^25 +371*x^24 +503*x^23 +628*x^22 +775*x^21 +895*x^20 +1023*x^19 +1099*x^18 +1167*x^17 +1172*x^16 +1161*x^15 +1087*x^14 +1007*x^13 +875*x^12 +754*x^11 +606*x^10 +483*x^9 +352*x^8 +258*x^7 +166*x^6 +109*x^5 +59*x^4 +34*x^3 +12*x^2 +7*x-1).

b:= proc(n, k, c, t) option remember;

`if`(n=0, 1, add(`if`(c=t and j=c, 0,

b(n-1, k, j, 1+`if`(j=c, t, 0))), j=1..k))

end:

a:= n-> b(n, 9, 0$2):

seq(a(n), n=0..30);

Geoffrey Critzer and Alois P. Heinz, <a href="/A242632/b242632.txt">Table of n, a(n) for n = 0..1000</a>

_Geoffrey Critzer_ and _Alois P. Heinz_, May 19 2014

Alois P. Heinz, <a href="/A242632/b242632.txt">Table of n, a(n) for n = 0..1000</a>

allocated for Alois P. Heinz

Number of n-length words w over a 9-ary alphabet {a_1,...,a_9} such that w contains never more than j consecutive letters a_j (for 1<=j<=9).

1, 9, 80, 711, 6318, 56143, 498896, 4433274, 39394819, 350068993, 3110771999, 27642843622, 245638961566, 2182789161071, 19396631915857, 172361736254288, 1531635402139359, 13610370004776711, 120944038906506659, 1074729088326395697, 9550223588843166996

0,2

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nonn

Alois P. Heinz, May 19 2014

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