OFFSET
0,1
COMMENTS
Second binomial transform of A135530.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
C. Bautista-Ramos and C. Guillen-Galvan, Fibonacci numbers of generalized Zykov sums, J. Integer Seq., 15 (2012), #12.7.8.
Index entries for linear recurrences with constant coefficients, signature (4, -2).
FORMULA
a(n) = 4*a(n-1) - 2*a(n-2) for n>1; a(0) = 2; a(1) = 5.
G.f.: (2-3*x)/(1-4*x+2*x^2).
MATHEMATICA
LinearRecurrence[{4, -2}, {2, 5}, 30] (* Harvey P. Dale, May 26 2012 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+r)*(2+r)^n+(4-r)*(2-r)^n)/4: n in [0..24] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009
(PARI) x='x+O('x^30); Vec((2-3*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Jan 27 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
EXTENSIONS
Edited and extended beyond a(4) by Klaus Brockhaus, Jul 01 2009
STATUS
approved