OFFSET
0,2
COMMENTS
The inverse binomial transform yields A030192. The binomial transform yields A162272. - R. J. Mathar, Jul 07 2009
LINKS
FORMULA
a(n) = 8*a(n-1) - 13(n-2) for n > 1; a(0) = 1, a(1) = 7.
G.f.: (1 - x)/(1 - 8*x + 13*x^2). - Klaus Brockhaus, Jun 19 2009
E.g.f.: exp(4*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - Stefano Spezia, Dec 31 2022
PROG
(PARI) F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((3+x)*(4+x)^n-(3-x)*(4-x)^n), (2*x))[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
(PARI) Vec((1-x)/(1-8*x+13*x^2)+O(x^25)) \\ M. F. Hasler, Dec 03 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
EXTENSIONS
Extended beyond a(5) by Klaus Brockhaus, Jun 19 2009
Edited by Klaus Brockhaus, Jul 05 2009; M. F. Hasler, Dec 03 2014
STATUS
approved