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A242629
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Number of n-length words w over a 6-ary alphabet {a_1,...,a_6} such that w contains never more than j consecutive letters a_j (for 1<=j<=6).
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2
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1, 6, 35, 204, 1188, 6919, 40295, 234672, 1366694, 7959418, 46354440, 269961210, 1572213035, 9156329637, 53325071447, 310557107219, 1808637367513, 10533228997581, 61343923944270, 357257684774972, 2080614429665859, 12117182049311250, 70568625653399251
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3,10,26,49,81,114,148,170,181,174,155,123,90,57,32,14,5).
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FORMULA
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G.f.: -(x^6+x^5+x^4+x^3+x^2+x+1) *(x+1)*(x^2-x+1) *(x^2+x+1) *(x^4+x^3+x^2+x+1) *(x^2+1) / (5*x^17 +14*x^16 +32*x^15 +57*x^14 +90*x^13 +123*x^12 +155*x^11 +174*x^10 +181*x^9 +170*x^8 +148*x^7 +114*x^6 +81*x^5 +49*x^4 +26*x^3 +10*x^2 +3*x-1).
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MAPLE
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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, 6, 0$2):
seq(a(n), n=0..30);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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