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

0,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Equals 4*A001353.

Sequence in context: A267928 A269532 A269673 * A128650 A072335 A081161

Adjacent sequences: A231893 A231894 A231895 * A231897 A231898 A231899

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 18 2013

Extensions

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

Status

approved