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A100545 Expansion of (7-2*x) / (x^2-3*x+1). 7
7, 19, 50, 131, 343, 898, 2351, 6155, 16114, 42187, 110447, 289154, 757015, 1981891, 5188658, 13584083, 35563591, 93106690, 243756479, 638162747, 1670731762, 4374032539, 11451365855, 29980065026, 78488829223, 205486422643, 537970438706, 1408424893475, 3687304241719, 9653487831682, 25273159253327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A Floretion integer sequence relating to Fibonacci numbers.

Inverse binomial transform of A013655; inversion of A097924.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Mark W. Coffey, James L. Hindmarsh, Matthew C. Lettington, John Pryce, On Higher Dimensional Interlacing Fibonacci Sequences, Continued Fractions and Chebyshev Polynomials, arXiv:1502.03085 [math.NT], 2015 (see p. 31).

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n-1) = 4*F(2n) + F(2n-1) + F(2n+1), F = A000045; a(n) + a(n+1) = A055849(n+2).

a(n) = 3*a(n-1)-a(n-2) with a(0)=7 and a(1)=19. - Philippe Deléham, Nov 16 2008

a(n) = (2^(-1-n)*((3-sqrt(5))^n*(-17+7*sqrt(5)) + (3+sqrt(5))^n*(17+7*sqrt(5)))) / sqrt(5). - Colin Barker, Oct 14 2015

MAPLE

F := proc(n) combinat[fibonacci](n) ; end: A100545 := proc(n) 4*F(2*(n+1))+F(2*n+1)+F(2*n+3) ; end: for n from 0 to 30 do printf("%d, ", A100545(n)) ; od ; # R. J. Mathar, Oct 26 2006

PROG

(PARI) Vec((7-2*x)/(x^2-3*x+1) + O(x^30)) \\ Michel Marcus, Feb 11 2015

CROSSREFS

Cf. A001906, A005248, A097924, A013655.

Sequence in context: A003232 A018728 A027523 * A203165 A100450 A155423

Adjacent sequences:  A100542 A100543 A100544 * A100546 A100547 A100548

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Dec 31 2004

EXTENSIONS

Corrected and extended by T. D. Noe and R. J. Mathar, Oct 26 2006

STATUS

approved

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Last modified January 21 15:09 EST 2017. Contains 281109 sequences.