OFFSET
0,1
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,1).
FORMULA
a(n) = 4*a(n-1) + a(n-2) for n > 1; a(0) = 4, a(1) = 13.
G.f.: (4-3*x)/(1-4*x-x^2).
a(n) = 2*A000032(3*n) + 5*A000045(3*n)/2 = 2*A014448(n) + 5*A001076(n). - Diego Rattaggi, Aug 09 2020
MATHEMATICA
LinearRecurrence[{4, 1}, {4, 13}, 30] (* Harvey P. Dale, Sep 19 2011 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((4+r)*(2+r)^n+(4-r)*(2-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009
(PARI) x='x+O('x^30); Vec((4-3*x)/(1-4*x-x^2)) \\ G. C. Greubel, Jan 08 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 21 2009
STATUS
approved