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A234312 Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, X. 10
1, 0, 2, 0, 4, 2, 8, 8, 16, 24, 36, 64, 88, 160, 224, 392, 576, 960, 1472, 2368, 3728, 5888, 9376, 14720, 23488, 36896, 58752, 92544, 146944, 232064, 367680, 581632, 920448, 1457152, 2305024, 3649664, 5773312, 9140224, 14460928, 22890496, 36221184, 57327616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,2)

FORMULA

G.f.: -1/(2*x^5+2*x^2-1).

a(n) = 2*(a(n-2)+a(n-5)) for n>4, a(1)=a(3)=0, a(0)=1, a(2)=2, a(4)=4.

EXAMPLE

a(4) = 4:

._______.  ._______.  ._______.  ._______.

|_. |_. |  | ._| ._|  |_. | ._|  | ._|_. |

| | | | |  | | | | |  | | | | |  | | | | |

| | | | |  | | | | |  | | | | |  | | | | |

| |_| |_|  |_| |_| |  | |_|_| |  |_| | |_|

|___|___|  |___|___|  |___|___|  |___|___|.

a(5) = 2:

._________.  ._________.

| | ._____|  |_____. | |

| |_| |_. |  | ._| |_| |

| |_. ._| |  | |_. ._| |

|___|_| | |  | | |_|___|

|_______|_|  |_|_______|.

MAPLE

a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>,

          <0|0|0|0|1>, <2|0|0|2|0>>^n)[5, 5]:

seq(a(n), n=0..50);

MATHEMATICA

LinearRecurrence[{0, 2, 0, 0, 2}, {1, 0, 2, 0, 4}, 50] (* Jean-Fran├žois Alcover, May 28 2019 *)

CROSSREFS

Cf. A077909, A174249, A233427, A234931, A247125, A264812.

Sequence in context: A278082 A327442 A068773 * A244136 A133168 A145382

Adjacent sequences:  A234309 A234310 A234311 * A234313 A234314 A234315

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 23 2013

STATUS

approved

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Last modified December 15 04:23 EST 2019. Contains 329991 sequences. (Running on oeis4.)