|
%I #40 Jan 05 2021 19:06:48
%S 0,4,16,60,224,836,3120,11644,43456,162180,605264,2258876,8430240,
%T 31462084,117418096,438210300,1635423104,6103482116,22778505360,
%U 85010539324,317263651936,1184044068420,4418912621744,16491606418556,61547513052480,229698445791364
%N a(n) = 4*a(n-1) - a(n-2) with a(0) = 0, a(1) = 4.
%C Number of domino tilings of a 2 X (2n-1) projective plane.
%C Numbers m such that 3*m^2+16 is a square. [_Bruno Berselli_, Dec 16 2014]
%H Colin Barker, <a href="/A231896/b231896.txt">Table of n, a(n) for n = 0..1000</a>
%H W. K. Alt, <a href="https://wyattalt.com/files/thesis.pdf">Enumeration of Domino Tilings on the Projective Grid Graph</a>, A Thesis Presented to The Division of Mathematics and Natural Sciences, Reed College, May 2013.
%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-1).
%F G.f.: 4*x/(1-4*x+x^2). - _Philippe Deléham_, Nov 19 2013
%F a(n) = ((2*(-(2-sqrt(3))^n+(2+sqrt(3))^n)))/sqrt(3). - _Colin Barker_, Oct 12 2015
%t LinearRecurrence[{4,-1},{0,4},30] (* _Harvey P. Dale_, Oct 01 2015 *)
%o (PARI) concat(0, Vec(4*x/(1-4*x+x^2) + O(x^40))) \\ _Colin Barker_, Oct 12 2015
%Y Equals 4*A001353.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 18 2013
%E More terms and other edits by _M. F. Hasler_, Nov 20 2013
|
