A233505 Number of tilings of a 2 X 2 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

1, 2, 9, 45, 201, 1062, 5564, 28859, 152012, 799387, 4202165, 22117465, 116385352, 612443308, 3223118545, 16961953022, 89264218645, 469766599585, 2472212575433, 13010374123502, 68468999197712, 360328057238019, 1896278913278432, 9979444454056631

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: (x^17 +3*x^16 -x^15 -5*x^14 +8*x^13 -8*x^12 -22*x^10 -20*x^9 -62*x^8 -20*x^7 -42*x^6 +18*x^5 +19*x^3 +x^2 +3*x -1) / (-x^20 -2*x^19 +2*x^18 +9*x^17 -12*x^16 +27*x^15 +41*x^14 +66*x^13 +62*x^12 +184*x^11 +76*x^10 +156*x^9 -92*x^8 +20*x^7 -141*x^6 +28*x^5 -62*x^4 +19*x^3 +5*x -1).

Maple

a:= n-> coeff(series((x^17 +3*x^16 -x^15 -5*x^14 +8*x^13 -8*x^12 -22*x^10 -20*x^9 -62*x^8 -20*x^7 -42*x^6 +18*x^5 +19*x^3 +x^2 +3*x -1)/(-x^20 -2*x^19 +2*x^18 +9*x^17 -12*x^16 +27*x^15 +41*x^14 +66*x^13 +62*x^12 +184*x^11 +76*x^10 +156*x^9 -92*x^8 +20*x^7 -141*x^6 +28*x^5 -62*x^4 +19*x^3 +5*x -1), x, n+1), x, n):
seq(a(n), n=0..40);

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233506, A233507, A233509.

Sequence in context: A059392 A264111 A264122 * A228767 A074607 A251178

Adjacent sequences: A233502 A233503 A233504 * A233506 A233507 A233508

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 11 2013

Status

approved