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Search: id:A146881
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| A146881 |
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A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]. |
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1
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| 1, 1, 1, 1, 8, 1, 1, 11, 11, 1, 1, 6, 12, 6, 1, 1, 9, 16, 16, 9, 1, 1, 12, 23, 22, 23, 12, 1, 1, 15, 25, 43, 43, 25, 15, 1, 1, 10, 30, 58, 76, 58, 30, 10, 1, 1, 13, 38, 86, 132, 132, 86, 38, 13, 1, 1, 16, 49, 122, 216, 254, 216, 122, 49, 16, 1
(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, 10, 24, 26, 52, 94, 168, 274, 540, 1062}.
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FORMULA
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p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{1}, {1, 1}, {1, 8, 1}, {1, 11, 11, 1}, {1, 6, 12, 6, 1}, {1, 9, 16, 16, 9, 1}, {1, 12, 23, 22, 23, 12, 1}, {1, 15, 25, 43, 43, 25, 15, 1}, {1, 10, 30, 58, 76, 58, 30, 10, 1}, {1, 13, 38, 86, 132, 132, 86, 38, 13, 1}, {1, 16, 49, 122, 216, 254, 216, 122, 49, 16, 1}
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MATHEMATICA
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Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n +Sum[(1 + Mod[Binomial[n, m], 4])*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: A021556 A109571 A133823 this_sequence A131067 A157170 A143679
Adjacent sequences: A146878 A146879 A146880 this_sequence A146882 A146883 A146884
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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 02 2008
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