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A158856
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A triangle of polynomial coefficients: p(x,n)=If[n == 0, 1, (Sum[x^i, {i, 0, Floor[(n - 1)/2] + 1}])(Sum[(-x)^i, {i, 0, Floor[n/2]}])].
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0
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1, 1, 1, 1, 0, -1, 1, 0, 0, -1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, -1, 0, -1, 1, 0, 1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{1, 2, 0, 0, 3, 4, 0, 0, 5, 6, 0...}.
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FORMULA
| p(x,n)=If[n == 0, 1, (Sum[x^i, {i, 0, Floor[(n - 1)/2] + 1}])(Sum[(-x)^i, {i, 0, Floor[n/2]}])];
t(n,m)=coefficients(p(x,n),x)
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EXAMPLE
| {1},
{1, 1},
{1, 0, -1},
{1, 0, 0, -1},
{1, 0, 1, 0, 1},
{1, 0, 1, 1, 0, 1},
{1, 0, 1, 0, -1, 0, -1},
{1, 0, 1, 0, 0, -1, 0, -1},
{1, 0, 1, 0, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 1, 0, 1, 0, 1},
{1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1}
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MATHEMATICA
| Clear[p, x, n, m, a];
p[x_, n_] = If[n == 0, 1, (Sum[x^i, {i, 0, Floor[(n - 1)/2] + 1}])(Sum[(-x)^i, {i, 0, Floor[n/2]}])];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A154957
Sequence in context: A103452 A131219 A127970 * A154957 A140865 A114000
Adjacent sequences: A158853 A158854 A158855 * A158857 A158858 A158859
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 28 2009
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