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 A213046 Convolution of Lucas numbers and positive integers repeated (A000032 and A008619). 1
 2, 3, 8, 13, 25, 41, 71, 116, 193, 314, 514, 834, 1356, 2197, 3562, 5767, 9339, 15115, 24465, 39590, 64067, 103668, 167748, 271428, 439190, 710631, 1149836, 1860481, 3010333, 4870829, 7881179, 12752024, 20633221, 33385262, 54018502, 87403782, 141422304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,1). FORMULA a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) + a(n-5). G.f.: (-2 + x)/((-1 + x)^2*(-1 + 2*x^2 + x^3)). a(n) = (-9/4 + (3*(-1)^n)/4 + (2^(-n)*((1-t)^n*(-5+2*t) + (1+t)^n*(5+2*t)))/t + (-1-n)/2) where t=sqrt(5). - Colin Barker, Feb 09 2017 MATHEMATICA f[x_] := (1 + x) (1 - x)^2; g[x] := 1 - x - x^2; s = Normal[Series[(2 - x)/(f[x] g[x]), {x, 0, 60}]] CoefficientList[s, x]  (* A213046 *) PROG (MAGMA) /* By definition */ A008619:=func; [&+[A008619(i)*Lucas(n-i): i in [0..n]]: n in [0..34]]; (PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, 0, -3, 1, 2]^n*[2; 3; 8; 13; 25])[1, 1] \\ Charles R Greathouse IV, Jan 29 2016 (PARI) Vec((-2 + x)/((-1 + x)^2*(-1 + 2*x^2 + x^3)) + O(x^60)) \\ Colin Barker, Feb 09 2017 CROSSREFS Cf. A213500. Sequence in context: A147417 A147357 A004138 * A262021 A221181 A116503 Adjacent sequences:  A213043 A213044 A213045 * A213047 A213048 A213049 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 10 2012 STATUS approved

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)