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A110515
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Sequence array for (1 - x + x^2 + x^3)/(1 - x^4).
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3
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1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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Riordan array ((1 - x + x^2 + x^3)/(1 - x^4), 1).
Column k has g.f. x^k*(1 - x + x^2 + x^3)/(1 - x^4).
T(n, k) = if(k <= n, -sin(Pi*(n-k)/2) + cos(Pi*(n-k))/2 + 1/2, 0).
T(n, k) = if(k <= n, Jacobi(2^(n-k), 2(n-k)+1), 0) [conjecture].
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EXAMPLE
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Rows begin
1;
-1, 1;
1, -1, 1;
1, 1, -1, 1;
1, 1, 1, -1, 1;
-1, 1, 1, 1, -1, 1;
1, -1, 1, 1, 1,- 1, 1;
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MATHEMATICA
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Table[If[k <= n, -Sin[Pi*(n - k)/2] + Cos[Pi*(n - k)]/2 + 1/2, 0], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Aug 29 2017 *)
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PROG
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(PARI) for(n=0, 20, for(k=0, n, print1(round(if(k<=n, -sin(Pi*(n-k)/2) + cos(Pi*(n-k))/2 + 1/2, 0)), ", "))) \\ G. C. Greubel, Aug 29 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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