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A091870 A trinomial transform of Fib(3n). 4
0, 1, 8, 53, 336, 2105, 13144, 81997, 511392, 3189169, 19888040, 124023461, 773419248, 4823095913, 30077155576, 187563189565, 1169656805184, 7294059356257, 45486249993032, 283655347025429, 1768894026280080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A084326. Second binomial transform of A001076(n)=Fib(3n)/2.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1258

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

Index entries for linear recurrences with constant coefficients, signature (8,-11)

FORMULA

G.f.: x/(1-8x+11x^2);

a(n) = sqrt(5)((4+sqrt(5))^n-(4-sqrt(5))^n)/10;

a(n) = sum{i=0..n, sum{j=0..n, n!/(i!j!(n-i-j)!)Fib(3i)/2}}.

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b-11*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)

CoefficientList[Series[x/(1 - 8 x + 11 x^2), {x, 0, 20}], x] (* Michael De Vlieger, Sep 22 2017 *)

PROG

(Sage) [lucas_number1(n, 8, 11) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 23 2009

CROSSREFS

Cf. A084326.

Sequence in context: A291662 A110099 A297334 * A252824 A054418 A293115

Adjacent sequences:  A091867 A091868 A091869 * A091871 A091872 A091873

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 06 2004

STATUS

approved

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Last modified February 23 15:20 EST 2018. Contains 299581 sequences. (Running on oeis4.)