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 A270062 Number of tilings of a 2 X n rectangle using monominoes and trominoes of any shape. 2
 1, 1, 5, 14, 45, 140, 438, 1371, 4287, 13413, 41956, 131249, 410572, 1284352, 4017713, 12568213, 39315905, 122988066, 384731445, 1203517448, 3764844982, 11777193395, 36841433019, 115247422841, 360517151000, 1127770261265, 3527892525112, 11035958382864 (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, Tromino Index entries for linear recurrences with constant coefficients, signature (1,5,5,1,-1,-1). FORMULA G.f.: -(x^3+x^2-1)/(x^6+x^5-x^4-5*x^3-5*x^2-x+1). a(n) = a(n-1) +5*(a(n-2)+a(n-3)) +a(n-4) -a(n-5) -a(n-6). EXAMPLE a(3) = 14: ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____. |_____|  |_|_|_|  |_____|  |_| |_|  | |_|_|  | ._|_|  |_. |_| |_____|  |_____|  |_|_|_|  |___|_|  |___|_|  |_|_|_|  |_|_|_| . ._____.  ._____.  ._____.  ._____.  ._____.  ._____.  ._____. |_|_|_|  | ._| |  | |_. |  |_|_| |  |_| |_|  |_| ._|  |_|_. | |_|_|_|  |_|___|  |___|_|  |_|___|  |_|___|  |_|_|_|  |_|_|_|  . . MAPLE a:= n-> (Matrix(6, (i, j)-> `if`(i+1=j, 1, `if`(i=6, [-1\$2, 1,          5\$2, 1][j], 0)))^n. <<1, 1, 5, 14, 45, 140>>)[1, 1]: seq(a(n), n=0..30); CROSSREFS Column k=2 of A270061. Sequence in context: A140796 A197212 A100059 * A236043 A270661 A222908 Adjacent sequences:  A270059 A270060 A270061 * A270063 A270064 A270065 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Mar 09 2016 STATUS approved

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Last modified January 15 12:06 EST 2021. Contains 340187 sequences. (Running on oeis4.)