A209971 a(n) = A000129(n) + n.

0, 2, 4, 8, 16, 34, 76, 176, 416, 994, 2388, 5752, 13872, 33474, 80796, 195040, 470848, 1136706, 2744228, 6625128, 15994448, 38613986, 93222380, 225058704, 543339744, 1311738146, 3166815988, 7645370072, 18457556080, 44560482178, 107578520380, 259717522880

Offset: 0

Author

N. J. A. Sloane, Mar 25 2012

Keywords

• nonn
• easy

References

• Paul Brickman, Problem in August 2011 issue of Fibonacci Quarterly. [Brickman has several problems in this issue, and I am not sure now which one I was referring to. - N. J. A. Sloane, Jan 22 2019]

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-4,0,1).

Crossrefs

Cf. A000129.

Programs

PARI

concat(0, Vec( 2*x*(1 - 2*x) / ((1 - x)^2*(1 - 2*x - x^2)) + O(x^50))) \\ Colin Barker, Nov 06 2017

Formula

G.f.: 2*x*(-1+2*x) / ( (x^2+2*x-1)*(x-1)^2 ). a(n) = 2*A100131(n-1). - R. J. Mathar, Mar 27 2012

From Colin Barker, Nov 06 2017: (Start)

a(n) = (-(1-sqrt(2))^n + (1+sqrt(2))^n) / (2*sqrt(2)) + n.

a(n) = 4*a(n-1) - 4*a(n-2) + a(n-4) for n>3.

(End)