A255496 3rd diagonal of triangle in A255494.

1, 38, 1106, 26544, 567203, 11179686, 207768576, 3692419776, 63361188037, 1057109514902, 17235551954894, 275697361933728, 4339725043253447, 67384965236252310, 1034147721558836220, 15711425790758327952, 236612932874975360809, 3536182524466029241958, 52494462902614684280330

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..850

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 (44,-649,2770,11885,-65240,-215431,-67286,139956,-23560,-2400).

Formula

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

a(n) = 12*a(n-1) + P(n+1)*A255495(n), where P(n) = A000129(n).

a(n) = (12)^(n+4) - (-2)^(n+1) - 2^n*Q(2*n+9) - 5^(n+4)*P(n+5) + (1/10)*P(n+4)*(P(n+4)^2 + (-1)^n), where P(n) = A000129(n), Q(n) = A002203(n).

G.f.: (1 -6*x +83*x^2 -228*x^3 -84*x^4 -200*x^5)/((1+2*x)*(1-12*x)*(1 +2*x -x^2)*(1 -10*x -25*x^2)*(1 -12*x +4*x^2)*(1 -14*x -x^2)). (End)

Mathematica

a[n_]:= (12)^(n+4) -(-2)^(n+1) -2^n*LucasL[2*n+9, 2] -5^(n+4)*Fibonacci[n+5, 2] +(1/10)*Fibonacci[n+4, 2]*(Fibonacci[n+4, 2]^2 +(-1)^n);
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Sep 20 2021 *)

Prog

(Sage)
def P(n): return lucas_number1(n, 2, -1)
def Q(n): return lucas_number2(n, 2, -1)
def a(n): return (12)^(n+4) - (-2)^(n+1) - 2^n*Q(2*n+9) - 5^(n+4)*P(n+5) + (1/10)*P(n+4)*(P(n+4)^2 + (-1)^n)
[a(n) for n in (0..30)] # G. C. Greubel, Sep 20 2021

Crossrefs

Cf. A000129, A002203, A255494, A255495.

Sequence in context: A028199 A285236 A208949 * A098612 A268739 A239043

Adjacent sequences: A255493 A255494 A255495 * A255497 A255498 A255499

Keyword

nonn

Author

N. J. A. Sloane, Mar 06 2015

Extensions

3 more terms. - R. J. Mathar, Jun 14 2015

Terms a(12) onward added by G. C. Greubel, Sep 20 2021

Status

approved