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A180672 a(n) = Fibonacci(n+7) - Fibonacci(7). 5
0, 8, 21, 42, 76, 131, 220, 364, 597, 974, 1584, 2571, 4168, 6752, 10933, 17698, 28644, 46355, 75012, 121380, 196405, 317798, 514216, 832027, 1346256, 2178296, 3524565, 5702874, 9227452, 14930339, 24157804, 39088156, 63245973 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The a(n+1) (terms doubled) are the Kn16 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..280

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

FORMULA

a(n) = F(n+7) - F(7) with F = A000045.

a(n) = a(n-1) + a(n-2) + 13 for n>1, a(0)=0, a(1)=8, and where 13 = F(7).

G.f.: x*(8 + 5*x)/((1 - x)*(1 - x - x^2)). - Ilya Gutkovskiy, Feb 24 2017

From Colin Barker, Feb 24 2017: (Start)

a(n) = (-13 + (2^(-1-n)*((1-sqrt(5))^n*(-29+13*sqrt(5)) + (1+sqrt(5))^n*(29+13*sqrt(5)))) / sqrt(5)).

a(n) = 2*a(n-1) - a(n-3) for n>2. (End)

a(n) = 8*A000071(n+2) + 5*A000071(n+1). - Bruno Berselli, Feb 24 2017

MAPLE

nmax:=40: with(combinat): for n from 0 to nmax do a(n):=fibonacci(n+7)-fibonacci(7) od: seq(a(n), n=0..nmax);

MATHEMATICA

Fibonacci[7 +Range[0, 40]] -13 (* G. C. Greubel, Jul 13 2019 *)

PROG

(MAGMA) [Fibonacci(n+7) - Fibonacci(7): n in [0..40]]; // Vincenzo Librandi, Apr 24 2011

(PARI) concat(0, Vec(x*(8+5*x)/((1-x)*(1-x-x^2)) + O(x^40))) \\ Colin Barker, Feb 24 2017

(PARI) a(n)=fibonacci(n+7)-fibonacci(7) \\ Charles R Greathouse IV, Feb 24 2017

(Sage) [fibonacci(n+7)-13 for n in (0..40)] # G. C. Greubel, Jul 13 2019

(GAP) List([0..40], n-> Fibonacci(n+7)-13 ); # 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: A275874 A190456 A188026 * A152117 A075629 A273602

Adjacent sequences:  A180669 A180670 A180671 * A180673 A180674 A180675

KEYWORD

nonn,easy

AUTHOR

Johannes W. Meijer, Sep 21 2010

STATUS

approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)