OFFSET
0,1
COMMENTS
Binomial transform of A163604.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-23).
FORMULA
a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 3, a(1) = 19.
G.f.: (3-11*x)/(1-10*x+23*x^2).
E.g.f.: exp(5*x)*( 3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017
MATHEMATICA
LinearRecurrence[{10, -23}, {3, 19}, 50] (* G. C. Greubel, Jul 29 2017 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+2*r)*(5+r)^n+(3-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 07 2009
(PARI) x='x+O('x^50); Vec((3-11*x)/(1-10*x+23*x^2)) \\ G. C. Greubel, Jul 29 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 07 2009
STATUS
approved