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A136395
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Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0,...].
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| 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
| 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
| 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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CROSSREFS
| Cf. A001263.
Sequence in context: A036837 A011851 A193912 * A014160 A014162 A014169
Adjacent sequences: A136392 A136393 A136394 * A136396 A136397 A136398
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 14 2008
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