A063651 Number of ways to tile a 7 X n rectangle with 1 X 1 and 2 X 2 tiles.

1, 1, 21, 85, 747, 4375, 31387, 202841, 1382259, 9167119, 61643709, 411595537, 2758179839, 18448963469, 123518353059, 826573277157, 5532716266089, 37028886137273, 247839719105625, 1658772577825883, 11102227136885119

Offset: 0

Author

Reiner Martin, Jul 23 2001

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,30,-17,-138,85,116,-42,-32).

Crossrefs

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

Column k=7 of A245013.

Formula

a(n) = 3a(n-1) + 30a(n-2) - 17a(n-3) - 138a(n-4) + 85a(n-5) + 116a(n-6) - 42a(n-7) - 32a(n-8). - Keith Schneider (kschneid(AT)bulldog.unca.edu), Apr 02 2006

G.f.: ( 1 -2*x -12*x^2 +9*x^3 +17*x^4 -6*x^5 -6*x^6 ) / ( 1 -3*x -30*x^2 +17*x^3 +138*x^4 -85*x^5 -116*x^6 +42*x^7 +32*x^8 ). - Colin Barker, Nov 29 2012