A251737 -id:A251737 - cp's OEIS frontend

A249762 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, I, L.

1, 1, 3, 5, 13, 50, 133, 360, 875, 2254, 6336, 17331, 47199, 124476, 330344, 889454, 2400961, 6485476, 17392906, 46616158, 125153478, 336529923, 905611165, 2434088873, 6539233985, 17567977887, 47214493386, 126927551197, 341177175540, 916960655233

Offset: 0

Alois P. Heinz, Dec 03 2014

nonn

			a(4) = 13:
._______.     ._______.     ._______.
| | | | |     | ._| ._|     | | ._| |
| | | | |     | |_. | |     | | | | |
| | | | |     | | |_| |     | | | | |
| | | | |     |_| ._| |     | |_| | |
|_|_|_|_| (1) |___|___| (2) |_|___|_| (2)
._______.     ._______.     ._______.
| ._| | |     | ._| ._|     | ._|_. |
| | | | |     | | | | |     | | | | |
| | | | |     | | | | |     | | | | |
|_| | | |     |_| |_| |     |_| | |_|
|___|_|_| (4) |___|___| (2) |___|___| (2) .

Alois P. Heinz, Table of n, a(n) for n = 0..1000
Vaclav Kotesovec, G.f. and the recurrence (of order 315)
Wikipedia, Pentomino

Cf. A174249, A233427, A247443, A247680, A251617, A251737, A257866, A264765.

a(n) ~ c * d^n, where d = 2.6877447474867836174937272605197376719631593933016281800670782370745298422..., c = 0.3236150736074998563483897952085529328299218049725560430481595704054051228... (1/d is the root of the denominator, see g.f.). - Vaclav Kotesovec, May 19 2015

A251617 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, I, L, U.

Original entry on oeis.org

1, 1, 3, 5, 19, 74, 219, 628, 1749, 5486, 17448, 53383, 160169, 479908, 1468366, 4512092, 13782535, 41855766, 127112554, 387469920, 1182800866, 3606789463, 10983721059, 33445214911, 101911804705, 310658892951, 946813182854, 2884825285301, 8789233684468

Offset: 0

Alois P. Heinz, Dec 05 2014

nonn

			a(4) = 19 = 13 + 4 + 2 = A249762(4) + 4 + 2:
._______.     ._______.
|_____. |     | ._____|
| | ._|_|     |_| ._. |
| | |_. |     | |_| |_|
| |___| |     |_____| |
|___|___| (4) |_______| (2) .

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

Cf. A174249, A233427, A247443, A247680, A249762, A251737.

cp's OEIS Frontend

A249762 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, I, L.

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