A159617 G.f.: (1-x)/(1-8*x-8*x^2+8*x^3).

1, 7, 64, 560, 4936, 43456, 382656, 3369408, 29668864, 261244928, 2300355072, 20255449088, 178356473856, 1570492542976, 13828748541952, 121767076888576, 1072202663100416, 9441127931576320, 83132508142305280, 732011467286249472

Offset

0,2

Comments

Number of tilings of a 2xn board with squares of 2 colors and dominoes of 2 colors if n>2. The number of tilings is 6 if n=1, and 56 if n=2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Katz, C. Stenson, Tiling a 2xn-board with squares and dominoes, J. Int. Seq. 12 (2009) # 09.2.2.

Index entries for linear recurrences with constant coefficients, signature (8,8,-8).

Formula

a(n) = 8*a(n-1) + 8*a(n-2) - 8*a(n-3) for n>2. - Colin Barker, Jul 05 2020

Mathematica

CoefficientList[Series[(1 - x)/(1 - 8 x - 8 x^2 + 8 x^3), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 11 2012 *)

Prog

(PARI) Vec((1 - x) / (1 - 8*x - 8*x^2 + 8*x^3) + O(x^25)) \\ Colin Barker, Jul 05 2020

Crossrefs

Cf. A030186, A102436, A159616.

Sequence in context: A027767 A055537 A333991 * A098307 A055995 A301424

Adjacent sequences: A159614 A159615 A159616 * A159618 A159619 A159620

Keyword

nonn,easy

Author

R. J. Mathar, Apr 17 2009

Status

approved