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 A099269 A sequence derived from a matrix using "0,1,2,3,4,5,6". 0
 1, 4, 32, 222, 1610, 11582, 83518, 601974, 4339414, 31280470, 225485414, 1625410326, 11716765478, 84460262198, 608831511430 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Recursion multipliers are seen in rightmost coefficients of the matrix characteristic polynomial, with changed signs: x^3 - 7x^2 - 4x + 18. a(n)/a(n-1) tends to 7.2084965573...a root of the polynomial and an eigenvalue of the matrix. LINKS Table of n, a(n) for n=1..15. Index entries for linear recurrences with constant coefficients, signature (7,4,-18). FORMULA Let M = the 3 X 3 matrix [4 5 6 / 2 3 0 / 1 0 0]. a(n) = rightmost term in M^n * [1 0 0]. a(n+3) = 7*a(n+2) + 4*a(n+1) - 18*a(n). G.f.: -x*(3*x-1) / (18*x^3-4*x^2-7*x+1). [Colin Barker, Dec 06 2012] EXAMPLE a(5) = 1610 since M^5 * [1 0 0] = [11582 5506 1610] a(9) = 4339414 = 7*601974 + 4*83518 - 18*11582 = 7*a(8) + 4*a(7) - 18*a(6). CROSSREFS Sequence in context: A298965 A316955 A299735 * A316810 A299656 A125823 Adjacent sequences: A099266 A099267 A099268 * A099270 A099271 A099272 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Oct 10 2004 STATUS approved

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Last modified May 30 07:21 EDT 2023. Contains 363045 sequences. (Running on oeis4.)