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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-François 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.)