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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

Table of n, a(n) for n=0..26.

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.)