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A213046
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Convolution of Lucas numbers and positive integers repeated (A000032 and A008619).
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1
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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
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OFFSET
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0,1
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(MAGMA) /* By definition */ A008619:=func<n | 1+Floor(n/2)>; [&+[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
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CROSSREFS
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Cf. A213500.
Sequence in context: A147417 A147357 A004138 * A262021 A221181 A116503
Adjacent sequences: A213043 A213044 A213045 * A213047 A213048 A213049
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 10 2012
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STATUS
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approved
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