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A242635
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Number of n-length words w over an n-ary alphabet {a_1,...,a_n} such that w contains never more than j consecutive letters a_j for 1<=j<=n.
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2
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1, 1, 3, 21, 208, 2631, 40295, 724892, 14984945, 350068993, 9121438862, 262285777567, 8250643190038, 281849526767134, 10390959086757005, 411219228179234026, 17387847546353549435, 782342249208357483984, 37321230268969840324231, 1881590248383756833279387
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = [x^n] 1/(1-Sum_{i=1..n} v(i)/(1+v(i))) with v(i) = (x-x^(i+1))/(1-x).
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MAPLE
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a:= proc(n) option remember; local v;
v:= i-> (x-x^(i+1))/(1-x);
coeff(series(1/(1-add(v(i)/(1+v(i)), i=1..n)), x, n+1), x, n)
end:
seq(a(n), n=0..25);
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MATHEMATICA
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b[n_, k_, c_, t_] := b[n, k, c, t] = If[n == 0, 1, Sum[If[c == t && j == c, 0, b[n - 1, k, j, 1 + If[j == c, t, 0]]], {j, 1, k}]];
a[n_] := b[n, n, 0, 0];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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