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A034299
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Alternating sum transform (PSumSIGN) of A000975.
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5
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1, 1, 4, 6, 15, 27, 58, 112, 229, 453, 912, 1818, 3643, 7279, 14566, 29124, 58257, 116505, 233020, 466030, 932071, 1864131, 3728274, 7456536, 14913085, 29826157, 59652328, 119304642, 238609299
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1/(1-x^2))/(1-x-2x^2); a(n) = sum{k=0..n+1, A001045(k)*(1-(-1)^floor((n+k)/2))}; - Paul Barry, Apr 16 2005
a(n) = a(n-1) + 2*a(n-2) + (1 + (-1)^n) / 2. - Michael Somos, Jan 23 2014
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EXAMPLE
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G.f. = 1 + x + 4*x^2 + 6*x^3 + 15*x^4 + 27*x^5 + 58*x^6 + 112*x^7 + ...
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MATHEMATICA
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CoefficientList[Series[(1/(1-x^2))/(1-x-2x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 04 2012 *)
Table[(2^(n + 5) + (6 n + 13) (-1)^n - 9)/36, {n, 0, 28}] (* Bruno Berselli, Apr 04 2012 *)
LinearRecurrence[{1, 3, -1, -2}, {1, 1, 4, 6}, 30] (* Harvey P. Dale, Jun 11 2019 *)
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PROG
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(PARI) {a(n) = (32 * 2^n - 9 + (6*n + 13) * (-1)^n) / 36}; /* Michael Somos, Jan 23 2014 */
(Magma) [(2^(n+5)+(6n+13)(-1)^n-9)/36: n in [0..50]]; // G. C. Greubel, Oct 12 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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