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A145131
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Expansion of x/((1 - x - x^4)*(1 - x)^2).
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5
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0, 1, 3, 6, 10, 16, 25, 38, 56, 81, 116, 165, 233, 327, 457, 637, 886, 1230, 1705, 2361, 3267, 4518, 6245, 8629, 11920, 16463, 22734, 31390, 43338, 59830, 82594, 114015, 157385, 217248, 299876, 413926, 571347, 788632, 1088546, 1502511, 2073898, 2862571
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OFFSET
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0,3
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COMMENTS
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The coefficients of the recursion for a(n) are given by the 3rd row of A145152.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = 3a(n-1) -3a(n-2) +a(n-3) +a(n-4) -2a(n-5) +a(n-6).
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EXAMPLE
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a(7) = 38 = 3*25 -3*16 +10 +6 -2*3 +1.
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MAPLE
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col:= proc(k) local l, j, M, n; l:= `if` (k=0, [1, 0, 0, 1], [seq (coeff ( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix (nops(l), (i, j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if` (k=0, n->(M^n)[2, 3], n->(M^n)[1, 2]) end: a:= col(3): seq (a(n), n=0..40);
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PROG
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(PARI) concat(0, Vec(1/(1-x-x^4)/(1-x)^2+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012
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CROSSREFS
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3rd column of A145153. Cf. A145152.
Sequence in context: A025222 A011902 A025004 * A152009 A114324 A054886
Adjacent sequences: A145128 A145129 A145130 * A145132 A145133 A145134
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KEYWORD
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nonn,easy
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AUTHOR
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Alois P. Heinz, Oct 03 2008
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STATUS
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approved
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