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A055819 Row sums of array T in A055818; twice the odd-index Fibonacci numbers after initial term. 7
1, 2, 4, 10, 26, 68, 178, 466, 1220, 3194, 8362, 21892, 57314, 150050, 392836, 1028458, 2692538, 7049156, 18454930, 48315634, 126491972, 331160282, 866988874, 2269806340, 5942430146, 15557484098, 40730022148, 106632582346 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Solutions (x, y) = (a(n), a(n+1)) satisfying x^2 + y^2 = 3xy - 4. - Michel Lagneau, Feb 01 2014

Except for the first term, positive values of x (or y) satisfying x^2 - 18xy + y^2 + 256 = 0. - Colin Barker, Feb 16 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Youngwoo Kwon, Binomial transforms of the modified k-Fibonacci-like sequence, arXiv:1804.08119 [math.NT], 2018.

D. Yaqubi, M. Farrokhi D.G., H. Gahsemian Zoeram, Lattice paths inside a table. I, arXiv:1612.08697 [math.CO], 2016-2017.

Index entries for linear recurrences with constant coefficients, signature (3,-1).

FORMULA

From Colin Barker, Feb 01 2014: (Start)

a(n) = 3*a(n-1) - a(n-2) for n > 0.

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

a(n) = 2*A001519(n) for n > 0. - Colin Barker, Feb 04 2014

MATHEMATICA

CoefficientList[Series[(1 - x - x^2)/(x^2 - 3 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 05 2014 *)

Join[{1}, LinearRecurrence[{3, -1}, {2, 4}, 30]] (* Harvey P. Dale, Oct 01 2014 *)

PROG

(PARI) Vec(-(x^2+x-1)/(x^2-3*x+1) + O(x^100)) \\ Colin Barker, Feb 01 2014

CROSSREFS

Essentially the same as A052995.

Sequence in context: A149810 A095337 A162533 * A052995 A113337 A084575

Adjacent sequences:  A055816 A055817 A055818 * A055820 A055821 A055822

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 28 2000

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)