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 A202536 Number of tilings of a 4 X n rectangle using straight (3 X 1) trominoes and 2 X 2 tiles. 3
 1, 0, 1, 3, 3, 8, 21, 31, 70, 165, 286, 615, 1351, 2548, 5353, 11343, 22320, 46349, 96516, 193944, 400313, 826747, 1678540, 3453642, 7105102, 14498569, 29781633, 61158957, 125108639, 256763850, 526846289, 1079030715, 2213527089, 4540131569, 9304062828 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: see Maple program. EXAMPLE a(3) = 3, because there are 3 tilings of a 4 X 3 rectangle using straight (3 X 1) trominoes and 2 X 2 tiles: ._____. ._____. ._._._. | | | | |_____| |_____| | | | | | | | | |_____| |_|_|_| | | | | |_____| |_____| |_|_|_| |_____| a(4) = 3, because there are 3 tilings of a 4 X 4 rectangle using straight (3 X 1) trominoes and 2 X 2 tiles: ._._____. ._____._. ._._._._. | |_____| |_____| | | . | . | | | . | | | | . | | |___|___| |_|___| | | |___|_| | . | . | |_____|_| |_|_____| |___|___| MAPLE gf:= -(x^3+x-1) *(x^18 -3*x^15 +x^14 +7*x^12 -3*x^11 -11*x^9 +3*x^8 +12*x^6 -x^5 -6*x^3+1) *(x-1)^2 *(x^2+x+1)^2 / (x^30 -x^29 +x^28 -5*x^27 +5*x^26 -4*x^25 +19*x^24 -12*x^23 +8*x^22 -56*x^21 +14*x^20 -10*x^19 +119*x^18 -2*x^17 +18*x^16 -174*x^15 -19*x^14 -35*x^13 +173*x^12 +31*x^11 +44*x^10 -115*x^9 -23*x^8 -29*x^7 +48*x^6 +8*x^5 +9*x^4 -11*x^3 -x^2 -x+1): a:= n-> coeff(series(gf, x, n+1), x, n); seq(a(n), n=0..50); CROSSREFS Cf. A165716, A165791, A165799, A190759, A219862. Column k=4 of A219967. Sequence in context: A049972 A027376 A190659 * A038068 A267952 A221773 Adjacent sequences: A202533 A202534 A202535 * A202537 A202538 A202539 KEYWORD nonn,nice AUTHOR Alois P. Heinz, Dec 20 2011 STATUS approved

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Last modified July 14 13:09 EDT 2024. Contains 374318 sequences. (Running on oeis4.)