OFFSET
0,1
COMMENTS
Binomial transform of A162396.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1)
FORMULA
a(n) = 2*a(n-1) + a(n-2) for n > 1; a(0) = 5, a(1) = 7.
G.f.: (5-3*x)/(1-2*x-x^2).
MATHEMATICA
LinearRecurrence[{2, 1}, {5, 7}, 30] (* Vincenzo Librandi, Feb 03 2018 *)
Table[(4*LucasL[n, 2] + LucasL[n + 1, 2])/2, {n, 0, 30}] (* G. C. Greubel, Aug 17 2018 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+r)*(1+r)^n+(5-r)*(1-r)^n)/2: n in [0..27] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 2009
(PARI) x='x+O('x^30); Vec((5-3*x)/(1-2*x-x^2)) \\ G. C. Greubel, Aug 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 02 2009
STATUS
approved