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 A100059 First differences of A052911. 2
 1, 5, 14, 45, 139, 434, 1351, 4209, 13110, 40837, 127203, 396226, 1234207, 3844441, 11975078, 37301261, 116189979, 361921042, 1127350583, 3511592833, 10938286998, 34071752661, 106130359315, 330586256610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)/a(n-1) tends to 3.11490754148...an eigenvalue of M and a root of the characteristic polynomial x^3 - 3x^2 - x + 2. REFERENCES Boris A. Bondarenko, "Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications"; Fibonacci Association, 1993, p. 27. LINKS Index entries for linear recurrences with constant coefficients, signature (3,1,-2). FORMULA G.f.: (2*x^2-2*x-1)*x / (-2*x^3+x^2+3*x-1). Recurrence: a(n) = 3*a(n-1) + a(n-2) - 2*a(n-3). a(n) = rightmost term in M^5 * [1 1 1], where M = the 3 X 3 upper triangular matrix [2 1 2 / 1 1 0 / 1 0 0]. INVERT transform of (1, 4, 5, 6, 7, 8, 9,...) with offset 0. EXAMPLE a(5) = 139 = rightmost term in M^5 * [1 1 1] which is [434 205 139]. 434 = a(6), while 205 = A052911(5). a(6) = 434 = 3*a(5) + a(4) - 2*a(3) = 3*139 + 45 - 2*14. MATHEMATICA LinearRecurrence[{3, 1, -2}, {1, 5, 14}, 30] (* Harvey P. Dale, Apr 21 2016 *) CROSSREFS Cf. A019481, A052550, A052939, A100058, A058071. Sequence in context: A302762 A140796 A197212 * A270062 A236043 A270661 Adjacent sequences:  A100056 A100057 A100058 * A100060 A100061 A100062 KEYWORD nonn AUTHOR Gary W. Adamson, Oct 31 2004 EXTENSIONS Edited by Ralf Stephan, Nov 02 2004 STATUS approved

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Last modified January 17 16:45 EST 2021. Contains 340247 sequences. (Running on oeis4.)