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A136395
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Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0, ...].
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1
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1, 4, 11, 25, 51, 96, 169, 281, 445, 676, 991, 1409, 1951, 2640, 3501, 4561, 5849, 7396, 9235, 11401, 13931, 16864, 20241, 24105, 28501, 33476, 39079, 45361, 52375, 60176, 68821, 78369, 88881, 100420, 113051, 126841, 141859, 158176, 175865, 195001
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OFFSET
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0,2
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LINKS
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FORMULA
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A007318 * [1, 3, 4, 3, 2, 0, 0, 0, ...]. A001263 * [1, 3, 1, 0, 0, 0, ...]
O.g.f.: -(1-x+x^2+x^4)/(-1+x)^5. - R. J. Mathar, Apr 02 2008
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EXAMPLE
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a(3) = 25 = (1, 3, 3, 1) dot (1, 3, 4, 3) = (1 + 9 + 12 + 3).
a(3) = 25 = (1, 6, 6, 1) dot (1, 3, 1, 0) = (1 + 18 + 6 + 0), where (1, 6, 6, 1) = row 4 of the Narayana triangle, A001263.
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MAPLE
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a := n-> (Matrix([[11, 4, 1, 1, 5]]). Matrix(5, (i, j)-> if (i=j-1) then 1 elif j=1 then [5, -10, 10, -5, 1][i] else 0 fi)^n)[1, 3]; seq (a(n), n=0..50); # Alois P. Heinz, Aug 14 2008
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MATHEMATICA
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CoefficientList[Series[-(1-x+x^2+x^4)/(-1+x)^5, {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 11, 25, 51}, 40] (* Harvey P. Dale, Dec 27 2016 *)
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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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EXTENSIONS
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STATUS
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approved
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