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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102902 a(n)=9a(n-1)-16a(n-2). 0
1, 9, 65, 441, 2929, 19305, 126881, 833049, 5467345, 35877321, 235418369, 1544728185, 10135859761, 66507086889, 436390025825, 2863396842201, 18788331166609, 123280631024265, 808912380552641, 5307721328585529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).

Index entries for linear recurrences with constant coefficients, signature (9,-16).

FORMULA

G.f.: 1/(1-9x+16x^2); a(n)=sum{k=0..n, binomial(2n-k+1, k)4^k}; a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-16)^k*9^(n-2k)}.

a(n)=-(9/34)*[9/2-(1/2)*sqrt(17)]^n*sqrt(17)+(9/34)*sqrt(17)*[9/2+(1/2)*sqrt(17)]^n+(1/2)*[9/2 -(1/2)*sqrt(17)]^n+(1/2)*[9/2+(1/2)*sqrt(17)]^n, with n>=0 - Paolo P. Lava, Jun 16 2008

MATHEMATICA

Join[{a=1, b=9}, Table[c=9*b-16*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)

LinearRecurrence[{9, -16}, {1, 9}, 20] (* Harvey P. Dale, Jul 28 2016 *)

PROG

(Sage) [lucas_number1(n, 9, 16) for n in xrange(1, 21)]# [From Zerinvary Lajos, Apr 23 2009]

CROSSREFS

Cf. A002540, A099459.

Sequence in context: A237040 A055284 A081040 * A127534 A037548 A238275

Adjacent sequences:  A102899 A102900 A102901 * A102903 A102904 A102905

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 17 2005

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 2 21:20 EST 2016. Contains 278694 sequences.