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A145132
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Expansion of x/((1 - x - x^4)*(1 - x)^3).
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5
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0, 1, 4, 10, 20, 36, 61, 99, 155, 236, 352, 517, 750, 1077, 1534, 2171, 3057, 4287, 5992, 8353, 11620, 16138, 22383, 31012, 42932, 59395, 82129, 113519, 156857, 216687, 299281, 413296, 570681, 787929, 1087805, 1501731, 2073078, 2861710, 3950256, 5452767
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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 4th row of A145152.
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LINKS
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FORMULA
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a(n) = 4a(n-1) -6a(n-2) +4a(n-3) -3a(n-5) +3a(n-6) -a(n-7).
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EXAMPLE
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a(8) = 155 = 4*99 -6*61 +4*36 -3*10 +3*4 -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(4): seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[x / ((1 - x - x^4) (1 - x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{4, -6, 4, 0, -3, 3, -1}, {0, 1, 4, 10, 20, 36, 61}, 40] (* Harvey P. Dale, Apr 04 2014 *)
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PROG
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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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