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A099453 Expansion of 1/(1-7x+11x^2). 8
1, 7, 38, 189, 905, 4256, 19837, 92043, 426094, 1970185, 9104261, 42057792, 194257673, 897167999, 4143341590, 19134543141, 88365044497, 408075336928, 1884511869029, 8702754376995, 40189650079646, 185597252410577 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Associated to the knot 8_12 by the modified Chebyshev transform A(x)-> (1/(1+x^2)^2)A(x/(1+x^2)). See A099454 and A099455.

LINKS

Table of n, a(n) for n=0..21.

Dror Bar-Natan, The Rolfsen Knot Table

S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.

J. Pan, Multiple Binomial Transforms and Families of Integer Sequences , J. Int. Seq. 13 (2010), 10.4.2, F^(3).

Index entries for linear recurrences with constant coefficients, signature (7,-11)

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)(-11)^k*7^(n-2k).

a(n) = ((7+sqrt(5))^n-(7-sqrt(5))^n)/(2^n*sqrt(5)), n > 0. Binomial transform of A030191 (Scaled Chebyshev U-polynomial evaluated at sqrt(5)/2); 3rd binomial transform of Fib(n). - Creighton Dement, Apr 19 2005

a(n) = 7*a(n-1) -11*a(n-2), n>=2. - Vincenzo Librandi, Mar 18 2011

MATHEMATICA

Join[{a=1, b=7}, Table[c=7*b-11*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)

PROG

(Sage) [lucas_number1(n, 7, 11) for n in xrange(1, 23)] # Zerinvary Lajos, Apr 23 2009

(PARI) Vec(1/(1-7*x+11*x^2) + O(x^40)) \\ Michel Marcus, Sep 09 2017

CROSSREFS

Sequence in context: A296769 A241524 A291822 * A292535 A026763 A217340

Adjacent sequences:  A099450 A099451 A099452 * A099454 A099455 A099456

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)