A255495 2nd diagonal of triangle in A255494.

1, 13, 130, 1106, 8575, 62475, 435576, 2939208, 19342285, 124800361, 792586270, 4969028750, 30822650251, 189500937303, 1156406300340, 7012380492516, 42294614785465, 253926386816725, 1518506730836026, 9050029200532298, 53778595325886295, 318762380704793571, 1885254096749834160

Offset

0,2

Links

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

S. Falcon, On The Generating Functions of the Powers of the K-Fibonacci Numbers, Scholars Journal of Engineering and Technology (SJET), 2014; 2 (4C):669-675.

Index entries for linear recurrences with constant coefficients, signature (14,-56,14,189,84,-20).

Formula

G.f.: (1 -x +4*x^2)/((1+x)*(1-5*x)*(1-6*x+x^2)*(1-4*x-4*x^2)). - R. J. Mathar, Jun 14 2015

From G. C. Greubel, Sep 20 2021: (Start)

a(n) = (1/2)*(P(n+3)*P(n+4) + 2^(n+4)*P(n+4) - 2*5^(n+3)), where P(n) = A000129(n).

a(n) = 5*a(n-1) + P(n+1)*(P(n+3) - 2^(n+2)) = 5*a(n) + P(n+1)*A094706(n+1). (End)

Mathematica

a[n_]:= (1/2)*(Fibonacci[n+3, 2]*Fibonacci[n+4, 2] + 2^(n+4)*Fibonacci[n+4, 2] - 2*5^(n+3));
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Sep 20 2021 *)

Prog

(Magma) I:=[1, 13, 130, 1106, 8575, 62475]; [n le 6 select I[n] else 14*Self(n-1) - 56*Self(n-2) +14*Self(n-3) +189*Self(n-4) + 84*Self(n-5) -20*Self(n-6): n in [1..31]]; // G. C. Greubel, Sep 20 2021
(Sage)
def P(n): return lucas_number1(n, 2, -1)
def A255495(n): return (1/2)*(P(n+3)*P(n+4) + 2^(n+4)*P(n+4) - 2*5^(n+3))
[A255495(n) for n in (0..30)] # G. C. Greubel, Sep 20 2021

Crossrefs

Cf. A000129, A094706, A255494.

Sequence in context: A016162 A155623 A023061 * A121033 A006100 A037603

Adjacent sequences: A255492 A255493 A255494 * A255496 A255497 A255498

Keyword

nonn

Author

N. J. A. Sloane, Mar 06 2015

Extensions

Terms a(13) onward from G. C. Greubel, Sep 20 2021

Status

approved