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A015456
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Generalized Fibonacci numbers.
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5
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1, 1, 11, 111, 1121, 11321, 114331, 1154631, 11660641, 117761041, 1189271051, 12010471551, 121293986561, 1224950337161, 12370797358171, 124932923918871, 1261700036546881, 12741933289387681, 128681032930423691, 1299552262593624591, 13124203658866669601
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = 10*a(n-1) + a(n-2).
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
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MATHEMATICA
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CoefficientList[Series[(1-9*x)/(1-10*x-x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 19 2017 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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