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Search: id:A146967
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| A146967 |
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A polynomial based symmetrical sequence: p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(2^(m - 1) +n*m - n + 1)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 34, 34, 34, 1, 1, 109, 102, 102, 109, 1, 1, 350, 303, 292, 303, 350, 1, 1, 1127, 901, 819, 819, 901, 1127, 1, 1, 3688, 2716, 2296, 2182, 2296, 2716, 3688, 1, 1, 12425, 8420, 6548, 5822, 5822, 6548, 8420, 12425, 1, 1, 43402
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:{1, 2, 6, 24, 104, 424, 1600, 5696, 19584, 66432, 226304}.
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FORMULA
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p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(2^(m - 1) +n*m - n + 1)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=Coefficients(p(x,m)).
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EXAMPLE
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{1}, {1, 1}, {1, 4, 1}, {1, 11, 11, 1}, {1, 34, 34, 34, 1}, {1, 109, 102, 102, 109, 1}, {1, 350, 303, 292, 303, 350, 1}, {1, 1127, 901, 819, 819, 901, 1127, 1}, {1, 3688, 2716, 2296, 2182, 2296, 2716, 3688, 1}, {1, 12425, 8420, 6548, 5822, 5822, 6548, 8420, 12425, 1}, {1, 43402, 27181, 19320, 15826, 14844, 15826, 19320, 27181, 43402, 1}
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MATHEMATICA
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Clear[p, x, n]; p[x_, n_] = If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[(2^(m - 1) + n*m - n + 1)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A156534 A008292 A157221 this_sequence A156049 A101919 A055106
Adjacent sequences: A146964 A146965 A146966 this_sequence A146968 A146969 A146970
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 03 2008
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