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A015457
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Generalized Fibonacci numbers.
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8
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1, 1, 12, 133, 1475, 16358, 181413, 2011901, 22312324, 247447465, 2744234439, 30434026294, 337518523673, 3743137786697, 41512034177340, 460375513737437, 5105642685289147, 56622445051918054, 627952538256387741, 6964100365872183205, 77233056562850402996
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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 11^k*binomial(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,...,11} containing no subwords ii, (i=0,1,...,10). - Milan Janjic, Jan 31 2015
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LINKS
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FORMULA
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a(n) = 11*a(n-1) + a(n-2).
For n>=2, a(n) = F_n(11)+F_(n+1)(11), where F_n(x) is Fibonacci polynomial (cf. A049310): F_n(x) = Sum_{i=0..floor((n-1)/2)} binomial(n-i-1,i)*x^(n-2*i-1). - Vladimir Shevelev, Apr 13 2012
a(n) = (F(5*n-5) + F(5*n))/5 for F(n) the Fibonacci sequence A000045(n). - Greg Dresden, Aug 22 2021
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MATHEMATICA
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CoefficientList[Series[(1-10*x)/(1-11*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 11*Self(n-1) + Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 08 2012
(PARI) x='x+O('x^30); Vec((1-10*x)/(1-11*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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