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A117441
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Periodic with period {1,1,0,1,-1,0,-1,-1,0,-1,1,0}.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Diagonal sums of number triangle A117440.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,1,0,-1).
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FORMULA
| 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)}.
a(n)=(1/12)*{-(n mod 12)+[(n+1) mod 12]-2*[(n+2) mod 12]+[(n+3) mod 12]-[(n+4) mod 12]+[(n+6) mod 12]-[(n+7) mod 12]+2*[(n+8) mod 12]-[(n+9) mod 12]+[(n+10) mod 12]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 11 2007
a(1)=a(2)=1; a(n)=a(n-2)+(-1)^n*a(n-1) - José María Grau Ribas, Jan 08 2012
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MATHEMATICA
| 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 *)
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PROG
| (PARI) Vec((1+x-x^2)/(1-x^2+x^4)+O(x^99)) \\ Charles R Greathouse IV, Jan 10 2012
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CROSSREFS
| Sequence in context: A016118 A011646 A016350 * A049347 A010892 A091338
Adjacent sequences: A117438 A117439 A117440 * A117442 A117443 A117444
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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EXTENSIONS
| More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Sep 26 2011
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