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 A254600 Numbers of words on alphabet {0,1,...,10} with no subwords ii, for i from {0,1}. 7
 1, 11, 119, 1289, 13961, 151211, 1637759, 17738489, 192124721, 2080893611, 22538058599, 244108628489, 2643928812281, 28636265779211, 310158017102639, 3359306563039289, 36384487784316641, 394078636910520011, 4268246759164049879, 46229175323835178889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) equals the number of sequences over the alphabet {0,1,...,9,10} such that no two consecutive terms have distance 10. - David Nacin, Jun 02 2017 LINKS Colin Barker, Table of n, a(n) for n = 0..950 Index entries for linear recurrences with constant coefficients, signature (10,9). FORMULA G.f.: (1+x)/(1-10*x-9*x^2). a(n) = 10*a(n-1) + 9*a(n-2) with n>1, a(0) = 1, a(1) = 11. a(n) = ((5-sqrt(34))^n*(-6+sqrt(34)) + (5+sqrt(34))^n*(6+sqrt(34))) / (2*sqrt(34)). - Colin Barker, Jan 21 2017 a(n) = (-3*i)^(n-1) * (ChebyshevU(n-1, 5*i/3) - 3*i*ChebyshevU(n, 5*i/3)). - G. C. Greubel, Feb 13 2021 MATHEMATICA RecurrenceTable[{a[0]==1, a[1]==11, a[n]== 10a[n-1] +9a[n-2]}, a[n], {n, 0, 25}] Table[(-3 I)^(n-1)*(ChebyshevU[n-1, 5*I/3] - 3*I*ChebyshevU[n, 5*I/3]), {n, 0, 25}] (* G. C. Greubel, Feb 13 2021 *) PROG (Magma) [n le 1 select 11^n else 10*Self(n)+9*Self(n-1): n in [0..20]]; // Bruno Berselli, Feb 03 2015 (PARI) Vec((x+1) / (1-10*x-9*x^2) + O(x^30)) \\ Colin Barker, Jan 21 2017 (Sage) [(-3*i)^(n-1)*( chebyshev_U(n-1, 5*i/3) -3*i*chebyshev_U(n, 5*i/3) ) for n in (0..30)] # G. C. Greubel, Feb 13 2021 CROSSREFS Cf. A015591, A055099, A126473, A126501, A126528. Sequence in context: A044724 A125468 A163447 * A354906 A060499 A164828 Adjacent sequences: A254597 A254598 A254599 * A254601 A254602 A254603 KEYWORD nonn,easy AUTHOR Milan Janjic, Feb 02 2015 STATUS approved

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Last modified December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)