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A117441
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Periodic with repeating part {1,1,0,1,-1,0,-1,-1,0,-1,1,0}.
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4
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1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, 0, 1, -1, 0
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OFFSET
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0,1
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COMMENTS
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Diagonal sums of number triangle A117440.
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LINKS
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FORMULA
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G.f.: (1+x-x^2)/(1-x^2+x^4).
a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*(cos(Pi*(n-2k)/2)+sin(Pi*(n-2k)/2).
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EXAMPLE
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G.f. = 1 + x + x^3 - x^4 - x^6 - x^7 - x^9 + x^10 + x^12 + x^13 + x^15 + ...
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MATHEMATICA
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a[1] := 1; a[2] := 1; a[n_] := a[n] = a[n - 2] + (-1)^(n) a[n - 1]; Array[a, 100] (* José María Grau Ribas, Jan 08 2012 *)
PadRight[{}, 84, {1, 1, 0, 1, -1, 0, -1, -1, 0, -1, 1, 0}] (* Harvey P. Dale, Mar 30 2012 *)
a[ n_] := KroneckerSymbol[ -6, 2 n + 5]; (* Michael Somos, Jul 18 2015 *)
LinearRecurrence[{0, 1, 0, -1}, {1, 1, 0, 1}, 78] (* Ray Chandler, Aug 25 2015 *)
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PROG
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(PARI) {a(n) = kronecker( -6, 2*n + 5)}; /* Michael Somos, Jul 18 2015 */
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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