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 A180674 a(n) = Fibonacci(n+9) - Fibonacci(9). 5
 0, 21, 55, 110, 199, 343, 576, 953, 1563, 2550, 4147, 6731, 10912, 17677, 28623, 46334, 74991, 121359, 196384, 317777, 514195, 832006, 1346235, 2178275, 3524544, 5702853, 9227431, 14930318, 24157783, 39088135, 63245952, 102334121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The a(n+1) (terms doubled) are the Kn18 sums of the Fibonacci(n) triangle A104763. See A180662 for information about these knight and other chess sums. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..275 Index entries for linear recurrences with constant coefficients, signature (2,0,-1). FORMULA a(n) = F(n+9) - F(9) with F = A000045. a(n) = a(n-1) + a(n-2) + 34 for n>1, a(0)=0, a(1)=21, and where 34 = F(9). G.f.: x*(21 + 13*x)/((1 - x)*(1 - x - x^2)). - Ilya Gutkovskiy, Feb 24 2017 a(n) = 21*A000071(n+2) + 13*A000071(n+1). - Bruno Berselli, Feb 24 2017 From Colin Barker, Feb 24 2017: (Start) a(n) = (-34 + (2^(-n)*((1-sqrt(5))^n*(-38+17*sqrt(5)) + (1+sqrt(5))^n*(38+17*sqrt(5)))) / sqrt(5)). a(n) = 2*a(n-1) - a(n-3) for n>2. (End) MAPLE nmax:=31: with(combinat): for n from 0 to nmax do a(n):=fibonacci(n+9)-fibonacci(9) od: seq(a(n), n=0..nmax); MATHEMATICA Fibonacci[9 +Range[0, 40]] -34 (* G. C. Greubel, Jul 13 2019 *) PROG (MAGMA) [Fibonacci(n+9) - Fibonacci(9): n in [0..40]]; // Vincenzo Librandi, Apr 24 2011 (PARI) concat(0, Vec(x*(21+13*x)/((1-x)*(1-x-x^2)) + O(x^40))) \\ Colin Barker, Feb 24 2017 (PARI) a(n) = fibonacci(n+9) - fibonacci(9) \\ Charles R Greathouse IV, Feb 24 2017 (Sage) [fibonacci(n+9)-34 for n in (0..40)] # G. C. Greubel, Jul 13 2019 (GAP) List([0..40], n-> Fibonacci(n+9)-34); # G. C. Greubel, Jul 13 2019 CROSSREFS Cf. A000045, A000071. Cf. A131524 (Kn11), A001911 (Kn12), A006327 (Kn13), A167616 (Kn14), A180671 (Kn15), A180672 (Kn16), A180673 (Kn17), A180674 (Kn18). Sequence in context: A190664 A144302 A347373 * A067431 A083676 A264104 Adjacent sequences:  A180671 A180672 A180673 * A180675 A180676 A180677 KEYWORD nonn,easy AUTHOR Johannes W. Meijer, Sep 21 2010 STATUS approved

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Last modified September 25 23:09 EDT 2021. Contains 347664 sequences. (Running on oeis4.)