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 A123108 a(n) = a(n-1) + a(n-2) - a(n-3), for n > 3, with a(0)=1, a(1)=0, a(2)=1, a(3)=1. 4
 1, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Diagonal sums of triangle A123110. - Philippe Deléham, Oct 08 2009 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA G.f.: (1 -x +x^3)/(1 -x -x^2 +x^3). a(n) = A110654(n-1). - R. J. Mathar, Jun 18 2008 a(n) = (1/4)*(1 + (-1)^n) + (1/2)*(n-1) + (binomial(2*n,n) mod 2). - Paolo P. Lava, Nov 19 2008 From G. C. Greubel, Jul 21 2021: (Start) a(n) = (1/4)*(2*n - 1 + (-1)^n) + [n=0]. E.g.f.: (1/2)*(2 + x*cosh(x) + (x-1)*sinh(x)). (End) MATHEMATICA LinearRecurrence[{1, 1, -1}, {1, 0, 1, 1}, 90] (* Harvey P. Dale, Aug 10 2020 *) PROG (Magma) I:=[0, 1, 1]; [1] cat [n le 3 select I[n] else Self(n-1) +Self(n-2) -Self(n-3): n in [1..31]]; // G. C. Greubel, Jul 21 2021 (Sage) [(2*n - 1 + (-1)^n)/4 + bool(n==0) for n in (0..90)] # G. C. Greubel, Jul 21 2021 CROSSREFS Cf. A065033, A110654, A123110. Sequence in context: A080513 A004526 A140106 * A008619 A110654 A350899 Adjacent sequences: A123105 A123106 A123107 * A123109 A123110 A123111 KEYWORD nonn,easy AUTHOR Philippe Deléham, Sep 28 2006 STATUS approved

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Last modified November 30 19:18 EST 2023. Contains 367462 sequences. (Running on oeis4.)