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 A132357 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4). 4
 1, 4, 14, 41, 122, 364, 1093, 3280, 9842, 29525, 88574, 265720, 797161, 2391484, 7174454, 21523361, 64570082, 193710244, 581130733, 1743392200, 5230176602, 15690529805, 47071589414, 141214768240, 423644304721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paolo Xausa, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3). FORMULA O.g.f.: -(1+x+2*x^2)/((3*x-1)*(x+1)*(x^2-x+1)) = -(3/2)/(3*x-1)+(1/3)*(x-2)/(x^2-x+1)+(1/ 6)/(x+1). - R. J. Mathar, Nov 28 2007 a(n) = (1/2)*3^(n+1) + (1/6)*(-1)^n - (2/3)*cos(Pi*n/3). Or, a(n) = (1/2)*3^(n+1) + (1/2)*[ -1; -1; 1; 1; 1; -1]. - Richard Choulet, Jan 02 2008 a(n+1) - 3a(n) = A132367(n+1). - Paul Curtz, Dec 02 2007 6*a(n) = (-1)^n +3^(n+2) -2*A057079(n+1). - R. J. Mathar, Oct 03 2021 MATHEMATICA LinearRecurrence[{3, 0, -1, 3}, {1, 4, 14, 41}, 50] (* Paolo Xausa, Dec 05 2023 *) PROG (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 3, -1, 0, 3]^n*[1; 4; 14; 41])[1, 1] \\ Charles R Greathouse IV, Oct 08 2016 CROSSREFS First differences of A132353. Cf. A129339. Sequence in context: A196713 A358587 A237853 * A262875 A219867 A295201 Adjacent sequences: A132354 A132355 A132356 * A132358 A132359 A132360 KEYWORD nonn,easy AUTHOR Paul Curtz, Nov 24 2007 STATUS approved

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Last modified May 25 07:15 EDT 2024. Contains 372782 sequences. (Running on oeis4.)