A063652 Number of ways to tile an 8 X n rectangle with 1 X 1 and 2 X 2 tiles.

1, 1, 34, 171, 2115, 16334, 159651, 1382259, 12727570, 113555791, 1029574631, 9258357134, 83605623809, 753361554685, 6795928721858, 61270295494859, 552555688390363, 4982395765808506, 44929655655496287, 405145692220245539, 3653405881837027898

Offset

0,3

Links

Table of n, a(n) for n=0..20.

S. Butler and S. Osborne, Counting tilings by taking walks, 2012. - From N. J. A. Sloane, Dec 27 2012

R. J. Mathar, Tiling nXm rectangles with 1X1 and sXs squares, arXiv:1609.03964 (2016) Section 4.1

Index entries for linear recurrences with constant coefficients, signature (6, 50, -171, -514, 1800, 845, -5430, 704, 6175, -1762, -2810, 870, 392, -120).

Formula

a(n) = 6a(n-1) + 50a(n-2) - 171a(n-3) - 514a(n-4) + 1800a(n-5) + 845a(n-6) - 5430a(n-7) + 704a(n-8) + 6175a(n-9) - 1762a(n-10) - 2810a(n-11) + 870a(n-12) + 392a(n-13) - 120a(n-14). - Keith Schneider (kschneid(AT)bulldog.unca.edu), Apr 02 2006

G.f.: ( 1 -5*x -22*x^2 +88*x^3 +74*x^4 -378*x^5 -31*x^6 +597*x^7 -114*x^8 -336*x^9 +94*x^10 +52*x^11 -16*x^12 ) / ( 1 -6*x -50*x^2 +171*x^3 +514*x^4 -1800*x^5 -845*x^6 +5430*x^7 -704*x^8 -6175*x^9 +1762*x^10 +2810*x^11 -870*x^12 -392*x^13 +120*x^14 ). - R. J. Mathar, Dec 19 2015

Crossrefs

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

Column k=8 of A245013.

Sequence in context: A182585 A191593 A259944 * A259886 A365222 A032771

Adjacent sequences: A063649 A063650 A063651 * A063653 A063654 A063655

Keyword

nonn

Author

Reiner Martin, Jul 23 2001

Status

approved