A063650 Number of ways to tile a 6 X n rectangle with 1 X 1 and 2 X 2 tiles.

1, 1, 13, 43, 269, 1213, 6427, 31387, 159651, 795611, 4005785, 20064827, 100764343, 505375405, 2536323145, 12724855013, 63851706457, 320373303983, 1607526474153, 8065864257905, 40471399479495, 203068825478591, 1018918472214687, 5112520236292975, 25652573037707685

Offset: 0

Author

Reiner Martin, Jul 23 2001

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• R. J. Mathar, Tiling nXm rectangles with 1X1 and sXs squares arXiv:1609.03964 [math.CO] (2016) Section 4.1.
• Index entries for linear recurrences with constant coefficients, signature (2,16,1,-27,1,4).

Crossrefs

Cf. A001045, A054854, A054855, A063650-A063654.

Column k=6 of A245013.

Programs

Magma

I:=[1,1,13,43,269,1213]; [n le 6 select I[n] else 2*Self(n-1)+16*Self(n-2)+Self(n-3)-27*Self(n-4)+Self(n-5)+4*Self(n-6): n in [1..30]]; // Vincenzo Librandi, Oct 30 2018

Mathematica

LinearRecurrence[{2, 16, 1, -27, 1, 4}, {1, 1, 13, 43, 269, 1213}, 22] (* Jean-François Alcover, Oct 30 2018 *)
CoefficientList[Series[(-1+x+5*x^2-x^4)/(-1+2*x+16*x^2+x^3-27*x^4+x^5+4*x^6), {x, 0, 50}], x] (* Stefano Spezia, Oct 30 2018 *)

Formula

G.f.: ( -1+x+5*x^2-x^4 ) / ( -1+2*x+16*x^2+x^3-27*x^4+x^5+4*x^6 ).

a(n) = 2a(n-1) + 16a(n-2) + a(n-3) - 27a(n-4) + a(n-5) + 4a(n-6) - Keith Schneider (kschneid(AT)bulldog.unca.edu), Apr 02 2006