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 A180673 a(n) = Fibonacci(n+8) - Fibonacci(8). 5
 0, 13, 34, 68, 123, 212, 356, 589, 966, 1576, 2563, 4160, 6744, 10925, 17690, 28636, 46347, 75004, 121372, 196397, 317790, 514208, 832019, 1346248, 2178288, 3524557, 5702866, 9227444, 14930331, 24157796, 39088148, 63245965, 102334134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The a(n+1) (terms doubled) are the Kn17 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+8) - F(8) with F(n) the Fibonacci numbers A000045. a(n) = a(n-1) + a(n-2) + 21 for n>1, a(0)=0, a(1)=13, and where 21 = F(8). G.f.: x*(13 + 8*x)/((1 - x)*(1 - x - x^2)). - Ilya Gutkovskiy, Feb 24 2017 a(n) = 13*A000071(n+2) + 8*A000071(n+1). - Bruno Berselli, Feb 24 2017 From Colin Barker, Feb 24 2017: (Start) a(n) = (-21 + (2^(-1-n)*((1-sqrt(5))^n*(-47+21*sqrt(5)) + (1+sqrt(5))^n*(47+21*sqrt(5)))) / sqrt(5)). a(n) = 2*a(n-1) - a(n-3) for n>2. (End) MAPLE nmax:=40: with(combinat): for n from 0 to nmax do a(n):=fibonacci(n+8)-fibonacci(8) od: seq(a(n), n=0..nmax); MATHEMATICA Fibonacci[8 +Range[0, 40]] -21 (* G. C. Greubel, Jul 13 2019 *) PROG (MAGMA [Fibonacci(n+8) - Fibonacci(8): n in [0..40]]; // Vincenzo Librandi, Apr 24 2011 (PARI) concat(0, Vec(x*(13+8*x)/((1-x)*(1-x-x^2)) + O(x^40))) \\ Colin Barker, Feb 24 2017 (PARI) a(n)=fibonacci(n+8)-21 \\ Charles R Greathouse IV, Feb 24 2017 (Sage) [fibonacci(n+8)-21 for n in (0..40)] # G. C. Greubel, Jul 13 2019 (GAP) List([0..40], n-> Fibonacci(n+8)-21) # 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: A292472 A081271 A190458 * A081752 A069484 A089113 Adjacent sequences:  A180670 A180671 A180672 * A180674 A180675 A180676 KEYWORD nonn,easy AUTHOR Johannes W. Meijer, Sep 21 2010 STATUS approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)