%I #28 Oct 30 2022 18:19:59
%S 1,1,55,341,5933,59925,795611,9167119,113555791,1355115601,
%T 16484061769,198549329897,2403674442213,29023432116879,
%U 350917980468767,4239961392742933,51247532773412135,619304595300705203,7484739788762129061,90454037365096154821
%N Number of ways to tile a 9 X n rectangle with 1 X 1 and 2 X 2 tiles.
%C a(8) is number of ways can kings be placed on an 8 X 8 chessboard so that no two kings can attack each other. - _Vaclav Kotesovec_, Apr 02 2010
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (6, 110, -262, -2786, 5916, 25168, -53907, -95299, 197820, 193866, -340168, -228528, 279636, 137864, -108909, -33736, 20214, 2460, -1296).
%F a(n) = 6*a(n-1) + 110*a(n-2) - 262*a(n-3) - 2786*a(n-4) + 5916*a(n-5) + 25168*a(n-6) - 53907*a(n-7) - 95299*a(n-8) + 197820*a(n-9) + 193866*a(n-10) - 340168*a(n-11) - 228528*a(n-12) + 279636*a(n-13) + 137864*a(n-14) - 108909*a(n-15) - 33736*a(n-16) + 20214*a(n-17) + 2460*a(n-18) - 1296*a(n-19).
%Y Cf. A001045, A054854, A054855, A063650, A063651, A063652, A063654.
%Y Column k=9 of A245013.
%K nonn
%O 0,3
%A _Reiner Martin_, Jul 23 2001
%E Subscripts in formula repaired by _Ron Hardin_, Dec 29 2010