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A099922 a(n) = F(4n) - 2n, where F(n) = Fibonacci numbers A000045. 1
1, 17, 138, 979, 6755, 46356, 317797, 2178293, 14930334, 102334135, 701408711, 4807526952, 32951280073, 225851433689, 1548008755890, 10610209857691, 72723460248107, 498454011879228, 3416454622906669, 23416728348467645 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 54.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,-16,9,-1)

FORMULA

G.f.: x*(1+8*x+x^2)/((1-x)^2 * (1-7*x+x^2)). [Corrected for offset by Georg Fischer, May 24 2019]

a(n) = Sum_{k=1..n} Lucas(2k-1)^2.

From Colin Barker, May 25 2019: (Start)

a(n) = (-((7-3*sqrt(5))/2)^n + ((7+3*sqrt(5))/2)^n)/sqrt(5) - 2*n.

a(n) = 9*a(n-1) - 16*a(n-2) + 9*a(n-3) - a(n-4) for n>4.

(End)

MATHEMATICA

Rest[CoefficientList[Series[x*(1+8x+x^2)/((1-x)^2*(1-7x+x^2)), {x, 0, 20}], x]] (* Georg Fischer, May 24 2019 *)

PROG

(PARI) Vec(x*(1 + 8*x + x^2) / ((1 - x)^2*(1 - 7*x + x^2)) + O(x^25)) \\ Colin Barker, May 25 2019

CROSSREFS

Equals A033888(n) - 2n. Partial sums of A081071. Bisection of A054452.

Sequence in context: A120784 A271395 A277387 * A298626 A157360 A142815

Adjacent sequences:  A099919 A099920 A099921 * A099923 A099924 A099925

KEYWORD

nonn

AUTHOR

Ralf Stephan, Nov 01 2004

STATUS

approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)