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 A187753 Number of different ways to divide an n X 5 rectangle into subsquares, considering only the list of parts. 2
 1, 1, 3, 5, 9, 11, 20, 26, 36, 48, 64, 80, 106, 128, 160, 195, 238, 281, 340, 397, 467, 544, 633, 724, 838, 950, 1083, 1226, 1385, 1550, 1745, 1942, 2165, 2402, 2663, 2933, 3242, 3555, 3902, 4270, 4667, 5079, 5539, 6007, 6518, 7055, 7631, 8227, 8880, 9547 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (x^9 - x^8 + x^7 - 4*x^6 + x^5 - 3*x^4 - x^3 - 2*x^2 - 1) / (x^19 - x^18 - x^16 + 2*x^12 + x^10 - x^9 - 2*x^7 + x^3 + x - 1). EXAMPLE a(4) = 9 because there are 9 ways to divide a 4 X 5 rectangle into subsquares, considering only the list of parts: [20(1 X 1)], [16(1 X 1), 1(2 X 2)], [12(1 X 1), 2(2 X 2)], [11(1 X 1), 1(3 X 3)], [8(1 X 1), 3(2 X 2)], [7(1 X 1), 1(2 X 2), 1(3 X 3)], [4(1 X 1), 4(2 X 2)], [4(1 X 1), 1(4 X 4)], [3(1 X 1), 2(2 X 2), 1(3 X 3)].  There is no way to divide this rectangle into [2(1 X 1), 2(3 X 3)]. MAPLE gf:= (x^9-x^8+x^7-4*x^6+x^5-3*x^4-x^3-2*x^2-1)/      (x^19-x^18-x^16+2*x^12+x^10-x^9-2*x^7+x^3+x-1): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=0..60); PROG (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x^2+x^3+3*x^4-x^5+4*x^6-x^7+x^8-x^9)/((1-x)^5*(1+x)^2*(1+x^2)*(1-x +x^2)*(1+x+x^2)^2*(1+x+x^2+x^3+x^4)))); // Bruno Berselli, Apr 17 2013 CROSSREFS Column k=5 of A224697. Sequence in context: A034760 A070639 A078392 * A231716 A113488 A092917 Adjacent sequences:  A187750 A187751 A187752 * A187754 A187755 A187756 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Apr 17 2013 STATUS approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)