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 A205492 Expansion of (1-x^2-x^3-x^4+x^5)/((1-x)^3*(1-x-x^2)^2*(1-2*x-x^2+x^3)). 0
 1, 7, 31, 109, 334, 937, 2475, 6267, 15393, 36976, 87369, 203915, 471546, 1082849, 2473535, 5627684, 12765052, 28887838, 65260270, 147233926, 331842395, 747355066, 1682185342, 3784718431, 8512408455, 19141037360, 43032743620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See array A205497 regarding association of this sequence with generating functions for the rows of the array form of A050446. LINKS L. E. Jeffery, Unit-primitive matrices Index entries for linear recurrences with constant coefficients, signature (7, -17, 12, 15, -26, 3, 13, -5, -2, 1). FORMULA a(n) = 7*a(n-1) - 17*a(n-2) + 12*a(n-3) + 15*a(n-4) - 26*a(n-5) + 3*a(n-6) + 13*a(n-7) - 5*a(n-8) - 2*a(n-9) + a(n-10), n>9, {a(m)} = {1, 7, 31, 109, 334, 937, 2475, 6267, 15393, 36976}, m=0,...,9. CONJECTURE 1. a(n) = M_{n,2} = M_{2,n}, where M = A205497. CONJECTURE 2. lim_{n -> infinity) a(n+1)/a(n) = (2*cos(Pi/7))^2-1 = A116425-1 = spectral radius of the 3 X 3 unit-primitive matrix (see [Jeffery]) A_{7,2} = [0,0,1; 0,1,1; 1,1,1]. MATHEMATICA LinearRecurrence[{7, -17, 12, 15, -26, 3, 13, -5, -2, 1}, {1, 7, 31, 109, 334, 937, 2475, 6267, 15393, 36976}, 30] (* Harvey P. Dale, Mar 26 2013 *) CROSSREFS A205497. Cf. A050446, A050447. Sequence in context: A119359 A055366 A160607 * A109756 A055580 A097786 Adjacent sequences:  A205489 A205490 A205491 * A205493 A205494 A205495 KEYWORD nonn AUTHOR L. Edson Jeffery, Jan 28 2012 STATUS approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)