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Search: id:A157896
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| A157896 |
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Coefficients of polynomials of a prime like factor set (skip power): p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2,2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}]; t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]]. |
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+0
1
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| 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Row sums are:
{1, 2, 8, 32, 50, 128, 200, 242, 392, 512, 648,...}.
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FORMULA
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p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2.2}];
q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}];
t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
out_(n,m)=coefficients(t(x,n)).
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EXAMPLE
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{1},
{1, 1},
{1, 1, 2, 2, 1, 1},
{1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1},
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1},
{1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1}
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MATHEMATICA
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Clear[p, q, t, x, n];
p[x_, n_] := Sum[x^i, {i, 0, (Prime[n] - 1)/2, 2}];
q[x_, n_] := Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2, 2}];
t[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
Table[ExpandAll[t[x, n]], {n, 0, 10, 2}];
Table[CoefficientList[ExpandAll[t[x, n]], x], {n, 0, 10, 2}];
Flatten[%]
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CROSSREFS
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Sequence in context: A140193 A073741 A071838 this_sequence A156072 A165031 A099245
Adjacent sequences: A157893 A157894 A157895 this_sequence A157897 A157898 A157899
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 08 2009
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