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 A353965 Number of tilings of a 3 X n rectangle using 2 X 2 and 1 X 1 tiles and right trominoes. 2
 1, 1, 13, 47, 259, 1189, 5877, 28167, 136723, 660173, 3194613, 15445007, 74699811, 361230229, 1746933205, 8448061879, 40854753875, 197572345789, 955455626773, 4620559362303, 22344915889827, 108059470995013, 522573007884725, 2527150465444071, 12221238828079379 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For tiling algorithm see A351322. LINKS Table of n, a(n) for n=0..24. Index entries for linear recurrences with constant coefficients, signature (3,9,-1,2). FORMULA G.f.: (1 - 2*x + x^2) / (1 - 3*x - 9*x^2 + x^3 - 2*x^4). a(n) = 3*a(n-1) + 9*a(n-2) - a(n-3) + 2*a(n-4). EXAMPLE a(2) = 13: v h,v h=v h,v ___ ___ ___ ___ ___ | | | |_| | _| | _| |_|_| mirroring included |___| |___| |_| | |_|_| |_|_| h: horizontal, v: vertical |_|_| |_|_| |___| |_|_| |_|_| 2 + 4 + 2 + 4 + 1 = 13 PROG (Maxima) See A352589. CROSSREFS Cf. A351322, A352589, A353963, A353964. Sequence in context: A358287 A146806 A300337 * A355961 A135712 A225920 Adjacent sequences: A353962 A353963 A353964 * A353966 A353967 A353968 KEYWORD nonn,easy AUTHOR Gerhard Kirchner, May 13 2022 STATUS approved

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Last modified October 4 19:37 EDT 2023. Contains 365888 sequences. (Running on oeis4.)