A231896 a(n) = 4*a(n-1) - a(n-2) with a(0) = 0, a(1) = 4.

0, 4, 16, 60, 224, 836, 3120, 11644, 43456, 162180, 605264, 2258876, 8430240, 31462084, 117418096, 438210300, 1635423104, 6103482116, 22778505360, 85010539324, 317263651936, 1184044068420, 4418912621744, 16491606418556, 61547513052480, 229698445791364

Offset: 0

Author

N. J. A. Sloane, Nov 18 2013

Keywords

• nonn
• easy

Comments

Number of domino tilings of a 2 X (2n-1) projective plane.

Numbers m such that 3*m^2+16 is a square. [Bruno Berselli, Dec 16 2014]

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• W. K. Alt, Enumeration of Domino Tilings on the Projective Grid Graph, A Thesis Presented to The Division of Mathematics and Natural Sciences, Reed College, May 2013.
• Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
• Index entries for linear recurrences with constant coefficients, signature (4,-1).

Crossrefs

Equals 4*A001353.

Programs

Mathematica

LinearRecurrence[{4,-1},{0,4},30] (* Harvey P. Dale, Oct 01 2015 *)

PARI

concat(0, Vec(4*x/(1-4*x+x^2) + O(x^40))) \\ Colin Barker, Oct 12 2015

Formula

G.f.: 4*x/(1-4*x+x^2). - Philippe Deléham, Nov 19 2013

a(n) = ((2*(-(2-sqrt(3))^n+(2+sqrt(3))^n)))/sqrt(3). - Colin Barker, Oct 12 2015

Extensions

More terms and other edits by M. F. Hasler, Nov 20 2013