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A146899
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A additive term polynomial as a stand alone polynomial: t0(n,m)=If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p(x,n)=Sum[t[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/(2*x)
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0
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1, 4, 4, 2, 3, 2, 6, 5, 5, 6, 3, 16, 10, 16, 3, 8, 22, 36, 36, 22, 8, 4, 14, 28, 35, 28, 14, 4, 10, 18, 42, 63, 63, 42, 18, 10, 5, 46, 60, 105, 126, 105, 60, 46, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Row sums are:{1, 8, 7, 22, 48, 132, 127, 266, 558}.
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FORMULA
| t0(n,m)=If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p(x,n)=Sum[t[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/(2*x); t(n,m)=coefficients(p(x,n)).
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EXAMPLE
| {1}, {4, 4}, {2, 3, 2}, {6, 5, 5, 6}, {3, 16, 10, 16, 3}, {8, 22, 36, 36, 22, 8}, {4, 14, 28, 35, 28, 14, 4}, {10, 18, 42, 63, 63, 42, 18, 10}, {5, 46, 60, 105, 126, 105, 60, 46, 5}
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MATHEMATICA
| Clear[t, p, x, n]; t[n_, m_] = If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p[x_, n_] = Sum[t[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/(2*x); Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Sequence in context: A002581 A161778 A099655 * A031351 A068923 A103714
Adjacent sequences: A146896 A146897 A146898 * A146900 A146901 A146902
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 02 2008
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