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 A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}. 1
 1, 10, 98, 962, 9442, 92674, 909602, 8927810, 87627106, 860066434, 8441614754, 82855064258, 813228496354, 7981896981250, 78342900802082, 768941283068738, 7547214754035298, 74076463050867586, 727065885490090658, 7136204673817756610, 70042369148280534754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of sequences over {0,1,...,9} of length n such that no two consecutive terms have distance 9. - David Nacin, May 31 2017 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,8). FORMULA a(n) = 9*a(n-1) + 8*a(n-2) with n>1, a(0) = 1, a(1) = 10. G.f.: (1 + x)/(1 - 9*x - 8*x^2). - Bruno Berselli, Feb 02 2015 a(n) = (2^(-1-n)*((9-r)^n*(-11+r) + (9+r)^n*(11+r))) / r, where r=sqrt(113). - Colin Barker, Jan 22 2017 MATHEMATICA RecurrenceTable[{a[0] == 1, a[1] == 10, a[n] == 9 a[n - 1] + 8 a[n - 2]}, a[n], {n, 0, 20}] (* Bruno Berselli, Feb 02 2015 *) PROG (MAGMA) [n le 1 select 10^n else 9*Self(n)+8*Self(n-1): n in [0..20]]; // Bruno Berselli, Feb 02 2015 (PARI) Vec((1 + x)/(1 - 9*x - 8*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017 CROSSREFS Cf. A015584, A055099, A126473, A126501, A126528. Sequence in context: A125445 A163446 A190869 * A217634 A007137 A135927 Adjacent sequences:  A254596 A254597 A254598 * A254600 A254601 A254602 KEYWORD nonn,easy AUTHOR Milan Janjic, Feb 02 2015 STATUS approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)