A361250 - OEIS

A361250

Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, N, X.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 8, 0, 18, 6, 16, 6, 48, 22, 74, 48, 182, 74, 306, 204, 544, 342, 1114, 826, 2038, 1546, 4144, 3126, 7452, 6470, 14538, 12542, 27824, 25994, 53398, 50244, 103288, 101306, 195756, 200120, 380310, 395802

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,11

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,1,0,3,-1,6,-2,0,-6,-1).

EXAMPLE

a(10) = 2:

.___________________.

|___. |_. ._| .___| |

|_. |___| |___|___ |

| |_____|_| |___. |_|

| .___| ._| |_. |___|

|_|_____|_____|_____| ... and its mirror.

a(14) = 2:

.___________________________.

|___. |_. ._| |_. ._| .___| |

|_. |___| |_. ._| |___|___ |

| |_____|_| |_| |_| |___. |_|

| .___| ._| |_. ._| |_. |___|

|_|_____|_____|_|_____|_____| ... and its mirror.

a(16) = 2:

._______________________________.

|___. |_. ._| .___|_. ._| .___| |

|_. |___| |___| .___| |___|___ |

| |_____|_| |___| ._|_| |___. |_|

| .___| ._| |_____| ._| |_. |___|

|_|_____|_____|_____|_____|_____| ... and its mirror.

a(17) = 2:

._________________________________.

|___. |_. ._| |___. |_. ._| .___| |

|_. |___| |_. ._| |___| |___|___ |

| |_____|_| |_|_. ._| |_| |___. |_|

| .___| ._| |_. |_|_. ._| |_. |___|

|_|_____|_____|_____|_|_____|_____| ... and its mirror.

MAPLE

gf:= (x^14+4*x^13+2*x^11-4*x^10+x^9-3*x^8-x^6-x^4-x^3+1)/

(x^14+6*x^13+2*x^11-6*x^10+x^9-3*x^8-x^6-x^4-x^3+1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..66);

CROSSREFS

Cf. A174249, A343529, A349187, A352421, A358933.

Sequence in context: A345060 A097106 A175801 * A165619 A368118 A328590

Adjacent sequences: A361247 A361248 A361249 * A361251 A361252 A361253

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Apr 20 2023

STATUS

approved