login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A081183 6th binomial transform of (0,1,0,2,0,4,0,8,0,16,...). 8
0, 1, 12, 110, 912, 7204, 55440, 420344, 3159168, 23618320, 176008128, 1309074656, 9724619520, 72186895936, 535605687552, 3972913788800, 29464372088832, 218493396246784, 1620132103941120, 12012809774902784, 89069225764835328 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (12,-34).

FORMULA

a(n) = 12*a(n-1) - 34*a(n-2) with n > 1, a(0)=0, a(1)=1.

G.f.: x/(1 - 12*x + 34*x^2).

a(n) = ((6 + sqrt(2))^n - (6 - sqrt(2))^n)/(2*sqrt(2)).

a(n) = Sum_{k=0..n} C(n,2k+1)*2^k*6^(n-2k-1).

E.g.f.: exp(6*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017

MATHEMATICA

CoefficientList[Series[x / (1 - 12 x + 34 x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)

PROG

(Sage) [lucas_number1(n, 12, 34) for n in xrange(0, 21)] /* Zerinvary Lajos, Apr 27 2009 */

(MAGMA) [n le 2 select n-1 else 12*Self(n-1)-34*Self(n-2): n in [1..25] ]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Binomial transform of A081182.

Sequence in context: A016214 A037581 A177071 * A069294 A000559 A037714

Adjacent sequences:  A081180 A081181 A081182 * A081184 A081185 A081186

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 16 10:36 EDT 2019. Contains 327094 sequences. (Running on oeis4.)