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 A015456 Generalized Fibonacci numbers. 5
 1, 1, 11, 111, 1121, 11321, 114331, 1154631, 11660641, 117761041, 1189271051, 12010471551, 121293986561, 1224950337161, 12370797358171, 124932923918871, 1261700036546881, 12741933289387681, 128681032930423691, 1299552262593624591, 13124203658866669601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n>=1, row sums of triangle for numbers 10^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,...,10} containing no subwords ii, (i=0,1,...,9). - Milan Janjic, Jan 31 2015 a(n) equals the number of sequences over the alphabet {0,1,...,9,10} such that no two consecutive terms have distance 6. - David Nacin, Jun 02 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 (10,1). FORMULA a(n) = 10*a(n-1) + a(n-2). a(n) = Sum_{k=0..n} 9^k*A055830(n,k). - Philippe Deléham, Oct 18 2006 a(n) = (1/2)*[5+sqrt(26)]^n-(1/13)*[5+sqrt(26)]^n*sqrt(26)+(1/2)*[5-sqrt(26)]^n+(1/13)*sqrt(26) *[5-sqrt(26)]^n, with n>=0. - Paolo P. Lava, Jul 15 2008 G.f.: (1-9*x)/(1-10*x-x^2). - Philippe Deléham, Nov 20 2008 For n>=2, a(n) = F_(n)(10) + F_(n+1)(10), 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 MATHEMATICA LinearRecurrence[{10, 1}, {1, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *) CoefficientList[Series[(1-9*x)/(1-10*x-x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 19 2017 *) PROG (MAGMA) [n le 2 select 1 else 10*Self(n-1) + Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 08 2012 (PARI) x='x+O('x^30); Vec((1-9*x)/(1-10*x-x^2)) \\ G. C. Greubel, Dec 19 2017 CROSSREFS Row m=10 of A135597. Sequence in context: A097115 A134732 A166747 * A240367 A199764 A097177 Adjacent sequences:  A015453 A015454 A015455 * A015457 A015458 A015459 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 18 08:12 EST 2018. Contains 318216 sequences. (Running on oeis4.)