OFFSET
1,2
COMMENTS
Preceded by zero, this is the eighth binomial transform of the Pell sequence A000129. - Sergio Falcon, Sep 21 2009; edited by Klaus Brockhaus, Oct 11 2009
Eighth binomial transform of A048697.
First differences are in A164600.
lim_{n -> infinity} a(n)/a(n-1) = 9 + sqrt(2) = 10.4142135623....
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..100
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 (18,-79).
FORMULA
a(n) = 18*a(n-1) - 79*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
G.f.: x/(1 - 18*x + 79*x^2). - Klaus Brockhaus, Dec 31 2008, corrected Oct 11 2009
a(n) = Sum[Binomial[n - 1 - i, i] (-1)^i * 18^(n - 1 - 2 i) * 79^i, {i, 0, Floor[(n - 1)/2]}]. - Sergio Falcon, Sep 21 2009
E.g.f.: exp(9*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017
MATHEMATICA
Join[{a=1, b=18}, Table[c=18*b-79*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{18, -79}, {1, 18}, 25] (* G. C. Greubel, Aug 22 2016 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Dec 31 2008
Edited by Klaus Brockhaus, Oct 11 2009
STATUS
approved