A027974 a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A027960.

1, 5, 14, 35, 81, 180, 389, 825, 1726, 3575, 7349, 15020, 30561, 61965, 125294, 252795, 509161, 1024100, 2057549, 4130225, 8284926, 16609455, 33282989, 66669660, 133507081, 267285605, 535010414, 1070731475, 2142612801

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Formula

a(n) = 8*2^n - Fibonacci(n+5) - Fibonacci(n+3).

a(n) = A101220(4, 2, n+1).

G.f.: (1+2*x)/((1-2*x)*(1-x-x^2)). - R. J. Mathar, Sep 22 2008

Maple

with(combinat); f:=fibonacci; seq(2^(n+3) - f(n+5) - f(n+3), n=0..30); # G. C. Greubel, Sep 26 2019

Mathematica

Table[2^(n+3) - LucasL[n+4], {n, 0, 30}] (* G. C. Greubel, Sep 26 2019 *)

Prog

(PARI) vector(31, n, f=fibonacci; 2^(n+2) - f(n+4) - f(n+2)) \\ G. C. Greubel, Sep 26 2019
(Magma) [2^(n+3) - Lucas(n+4): n in [0..30]]; // G. C. Greubel, Sep 26 2019
(Sage) [2^(n+3) - lucas_number2(n+4, 1, -1) for n in (0..30)] # G. C. Greubel, Sep 26 2019
(GAP) List([0..30], n-> 2^(n+3) - Lucas(1, -1, n+4)[2]); # G. C. Greubel, Sep 26 2019

Crossrefs

Cf. A000032, A000045, A027960.

Sequence in context: A335651 A066767 A227200 * A027983 A142585 A332743

Adjacent sequences: A027971 A027972 A027973 * A027975 A027976 A027977

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved