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A180671 a(n) = Fibonacci(n+6) - Fibonacci(6). 5
0, 5, 13, 26, 47, 81, 136, 225, 369, 602, 979, 1589, 2576, 4173, 6757, 10938, 17703, 28649, 46360, 75017, 121385, 196410, 317803, 514221, 832032, 1346261, 2178301, 3524570, 5702879, 9227457, 14930344, 24157809, 39088161, 63245978, 102334147, 165580133 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The a(n+1) (terms doubled) are the Kn15 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+6) - F(6) with F = A000045.

a(n) = a(n-1) + a(n-2) + 8 for n>1, a(0)=0, a(1)=5, and where 8 = F(6).

From Colin Barker, Apr 13 2012: (Start)

G.f.: x*(5 + 3*x)/((1 - x)*(1 - x - x^2)).

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

a(n) = (-8 + (2^(-n)*((1-sqrt(5))^n*(-9+4*sqrt(5)) + (1+sqrt(5))^n*(9+4*sqrt(5)))) / sqrt(5)). - Colin Barker, Apr 20 2017

MAPLE

nmax:=40: with(combinat): for n from 0 to nmax do a(n):=fibonacci(n+6)-fibonacci(6) od: seq(a(n), n=0..nmax);

MATHEMATICA

f[n_]:= Fibonacci[n+6] - Fibonacci[6]; Array[f, 40, 0] (* or *)

LinearRecurrence[{2, 0, -1}, {0, 5, 13}, 41] (* or *)

CoefficientList[Series[x(3x+5)/(x^3-2x+1), {x, 0, 40}], x] (* Robert G. Wilson v, Apr 11 2017 *)

PROG

(MAGMA) [Fibonacci(n+6)-Fibonacci(6): n in [0..40]]; // Vincenzo Librandi, Apr 24 2011

(PARI) for(n=1, 40, print(fibonacci(n+6)-fibonacci(6))); // Anton Mosunov, Mar 02 2017

(PARI) concat(0, Vec(x*(5+3*x)/((1-x)*(1-x-x^2)) + O(x^40))) \\ Colin Barker, Apr 20 2017

(Sage) [fibonacci(n+6)-8 for n in (0..40)] # G. C. Greubel, Jul 13 2019

(GAP) List([0..40], n-> Fibonacci(n+6)-8) # G. C. Greubel, Jul 13 2019

CROSSREFS

Cf. A000045.

Cf. A131524 (Kn11), A001911 (Kn12), A006327 (Kn13), A167616 (Kn14), A180671 (Kn15), A180672 (Kn16), A180673 (Kn17), A180674 (Kn18).

Sequence in context: A008778 A299277 A014813 * A211637 A256111 A322417

Adjacent sequences:  A180668 A180669 A180670 * A180672 A180673 A180674

KEYWORD

nonn,easy

AUTHOR

Johannes W. Meijer, Sep 21 2010

STATUS

approved

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Last modified April 10 06:23 EDT 2020. Contains 333392 sequences. (Running on oeis4.)