1,2

Number of domino tilings of a 2 X n strip on a cylinder.

Number of domino tilings of a 2 X n rectangle = Fibonacci(n) - see A000045.

Apart from initial terms, identical to A102081. - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jun 03 2006

S.-M. Belcastro, Tilings of 2 x n Grids on Surfaces, preprint.

H. Hosoya and F. Harary, On the matching properties of three fence graphs. J. Math. Chem., 12(1993), 211-218.

a(n) = F_(n+1) + F_(n-1) + 2 if n is even, a(n) = F_(n+1) + F_(n-1) if n is odd, where F(n) is the n-th Fibonacci number - sequence A000045.

a(n) = 1+(-1)^n+((1+sqrt(5))/2)^n+((1-sqrt(5))/2)^n = 1+(-1)^n+A000032(n). Recurrence: a(n) = a(n-1)+2*a(n-2)-a(n-3)-a(n-4). G.f.: (4-3*x-4*x^2+x^3)/(1-x-2*x^2+x^3+x^4). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 08 2002

((1 + Sqrt[5])/2)^n + ((1 - Sqrt[5])/2)^n + 1 + (-1)^n (from Hosoya/Harary)

a(1) = 1, a(2) = 5; a(n) = a(n - 1) + a(n - 2) - 2 Mod[n, 2]. (from Belcastro)

Cf. A000032, A000045.

Sequence in context: A054508 A110617 A102081 this_sequence A022344 A046588 A086654

Adjacent sequences: A068394 A068395 A068396 this_sequence A068398 A068399 A068400

nonn,easy

Sharon Sela (sharonsela(AT)hotmail.com), Mar 30 2002

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 08 2002

Two initial terms added, third comment amended to be consonant with new initial terms, offset changed to be consonant with initial terms, two references added, two formulae added. - Sarah-Marie Belcastro, Jul 04 2009