A063653 Number of ways to tile a 9 X n rectangle with 1 X 1 and 2 X 2 tiles.

1, 1, 55, 341, 5933, 59925, 795611, 9167119, 113555791, 1355115601, 16484061769, 198549329897, 2403674442213, 29023432116879, 350917980468767, 4239961392742933, 51247532773412135, 619304595300705203, 7484739788762129061, 90454037365096154821

Offset: 0

Author

Reiner Martin, Jul 23 2001

Keywords

• nonn

Comments

a(8) is number of ways can kings be placed on an 8 X 8 chessboard so that no two kings can attack each other. - Vaclav Kotesovec, Apr 02 2010

Links

• Index entries for linear recurrences with constant coefficients, signature (6, 110, -262, -2786, 5916, 25168, -53907, -95299, 197820, 193866, -340168, -228528, 279636, 137864, -108909, -33736, 20214, 2460, -1296).

Crossrefs

Cf. A001045, A054854, A054855, A063650, A063651, A063652, A063654.

Column k=9 of A245013.

Formula

a(n) = 6*a(n-1) + 110*a(n-2) - 262*a(n-3) - 2786*a(n-4) + 5916*a(n-5) + 25168*a(n-6) - 53907*a(n-7) - 95299*a(n-8) + 197820*a(n-9) + 193866*a(n-10) - 340168*a(n-11) - 228528*a(n-12) + 279636*a(n-13) + 137864*a(n-14) - 108909*a(n-15) - 33736*a(n-16) + 20214*a(n-17) + 2460*a(n-18) - 1296*a(n-19).

Extensions

Subscripts in formula repaired by Ron Hardin, Dec 29 2010