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 A034299 Alternating sum transform (PSumSIGN) of A000975. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 N. J. A. Sloane, Transforms Index entries for linear recurrences with constant coefficients, signature (1,3,-1,-2). FORMULA a(n) = sum{k=0..floor(n/2), A001045(n-2k+1)}. - Paul Barry, Nov 24 2003 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) = sum_{k, 0<=k<=n} A126258(n,k). - Philippe Deléham, Mar 13 2007 a(n) = 2*a(n-1)+A001057(n+1), with a(0)=1. - Bruno Berselli, Nov 09 2010 a(n) = (2^(n+5)+(6n+13)(-1)^n-9)/36. - Bruno Berselli, Apr 04 2012 a(n) = a(n-1) + 2*a(n-2) + (1 + (-1)^n) / 2. - Michael Somos, Jan 23 2014 A160156(n) = a(2*n). - Michael Somos, Oct 16 2020 EXAMPLE G.f. = 1 + x + 4*x^2 + 6*x^3 + 15*x^4 + 27*x^5 + 58*x^6 + 112*x^7 + ... MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A160156. Sequence in context: A045907 A254325 A351145 * A007135 A294070 A073603 Adjacent sequences:  A034296 A034297 A034298 * A034300 A034301 A034302 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified November 26 04:47 EST 2022. Contains 358353 sequences. (Running on oeis4.)