OFFSET
1,2
COMMENTS
Fourth binomial transform of A054489.
lim_{n -> infinity} a(n)/a(n-1) = 7 + 2*sqrt(2) = 9.8284271247....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (14,-41).
FORMULA
a(n) = 14*a(n-1) - 41*a(n-2) for n>1, with a(0)=0, a(1)=1. - Philippe Deléham, Jan 12 2009
G.f.: x/(1 - 14*x + 41*x^2). - Klaus Brockhaus, Jan 12 2009, corrected Oct 08 2009
E.g.f.: (1/4*sqrt(2))*exp(7*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 13 2016
MAPLE
A154347:=n->((7+2*sqrt(2))^n-(7-2*sqrt(2))^n)/(4*sqrt(2)): seq(simplify(A154347(n)), n=1..30); # Wesley Ivan Hurt, Sep 13 2016
MATHEMATICA
LinearRecurrence[{14, -41}, {1, 14}, 25] (* or *) Table[( (7 + 2*sqrt(2))^n - (7 - 2*sqrt(2))^n )/(4*sqrt(2)), {n, 1, 25}] (* G. C. Greubel, Sep 13 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((7+2*r)^n-(7-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009
Edited by Klaus Brockhaus, Oct 08 2009
STATUS
approved