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A145136
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Expansion of x/((1 - x - x^4)*(1 - x)^7).
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4
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0, 1, 8, 36, 120, 331, 801, 1761, 3597, 6931, 12737, 22506, 38479, 63974, 103843, 165109, 257852, 396439, 601229, 900934, 1335886, 1962555, 2859794, 4137468, 5948374, 8504704, 12100779, 17144439, 24200381, 34049989, 47773928, 66866159
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The coefficients of the recursion for a(n) are given by the 8th row of A145152.
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FORMULA
| a(0)=0, a(1)=1, a(2)=8, a(3)=36, a(4)=120, a(5)=331, a(6)=801, a(7)=1761, a(8)=3597, a(9)=6931, a(10)=12737, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)- 69*a(n-4) +49*a(n-5)-7*a(n-6)-27*a(n-7)+34*a(n-8)-21*a(n-9)+7*a(n-10)-a(n-11). [From Harvey P. Dale, Jan 03 2012]
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EXAMPLE
| a(n) = 8a(n-1) -28a(n-2) +56a(n-3) -69a(n-4) +49a(n-5) -7a(n-6) -27a(n-7) +34a(n-8) -21a(n-9) +7a(n-10) -a(n-11).
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MAPLE
| 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(8): seq (a(n), n=0..40);
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MATHEMATICA
| CoefficientList[Series[x/((1-x-x^4)*(1-x)^7), {x, 0, 40}], x] (* or *) LinearRecurrence[{8, -28, 56, -69, 49, -7, -27, 34, -21, 7, -1}, {0, 1, 8, 36, 120, 331, 801, 1761, 3597, 6931, 12737}, 40] (* From Harvey P. Dale, Jan 03 2012 *)
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CROSSREFS
| 8th column of A145153. Cf. A145152.
Sequence in context: A023033 A000580 A145457 * A144901 A054470 A131123
Adjacent sequences: A145133 A145134 A145135 * A145137 A145138 A145139
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 03 2008
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