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 A015454 Generalized Fibonacci numbers. 5
 1, 1, 9, 73, 593, 4817, 39129, 317849, 2581921, 20973217, 170367657, 1383914473, 11241683441, 91317382001, 741780739449, 6025563297593, 48946287120193, 397595860259137, 3229713169193289, 26235301213805449, 213112122879636881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)/a(n-1) tends to (8 + 2*sqrt(17))/2 = exp ArcSinh 4 = A176458. - Gary W. Adamson, Dec 26 2007 For n>=1, row sums of triangle for numbers 8^k*C(m,k) with duplicated diagonals. - Vladimir Shevelev, Apr 13 2012 For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,8} containing no subwords ii, (i=0,1,...,7). - Milan Janjic, Jan 31 2015 a(n+1) is the number of nonary sequences of length n such that no two consecutive terms have distance 5. - David Nacin, May 31 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7. Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (8,1) FORMULA a(n) = 8*a(n-1) + a(n-2). a(n) = Sum_{k=0..n} 7^k*A055830(n,k). - Philippe Deléham, Oct 18 2006 G.f.: (1-7*x)/(1-8*x-x^2). - Philippe Deléham, Nov 20 2008 a(n) = (3/34)*sqrt(17)*[4-sqrt(17)]^n-(3/34)*[4+sqrt(17)]^n*sqrt(17)+(1/2)*[4+sqrt(17)]^n+(1/2) *[4-sqrt(17)]^n, with n>=0. - Paolo P. Lava, Nov 21 2008 For n>=2, a(n) = F_n(8)+F_(n+1)(8), where F_n(x) is Fibonacci polynomial (cf.A049310): F_n(x) = Sum_{i=0..floor((n-1)/2)} C(n-i-1,i)*x^(n-2*i-1). - Vladimir Shevelev, Apr 13 2012 a(n) = A041025(n) -7*A041025(n-1). - R. J. Mathar, Jul 06 2012 MATHEMATICA LinearRecurrence[{8, 1}, {1, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *) CoefficientList[Series[(1-7*x)/(1-8*x-x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 19 2017 *) PROG (MAGMA) [n le 2 select 1 else 8*Self(n-1) + Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 08 2012 (PARI) x='x+O('x^30); Vec((1-7*x)/(1-8*x-x^2)) \\ G. C. Greubel, Dec 19 2017 CROSSREFS Row m=8 of A135597. Sequence in context: A164588 A023001 A277672 * A121246 A086226 A199677 Adjacent sequences:  A015451 A015452 A015453 * A015455 A015456 A015457 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 11 07:29 EST 2019. Contains 329914 sequences. (Running on oeis4.)