OFFSET
1,2
COMMENTS
Conjecture: for odd primes p, p divides a(p). Note that (a(n)) and A001333 have different offsets.
The conjecture follows from the formula A001333(n) = ((1-sqrt(2))^n + (1+sqrt(2))^n)/2. - Max Alekseyev, Oct 16 2005
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,5,2).
FORMULA
From Colin Barker, Apr 30 2019: (Start)
G.f.: x^2*(5 + 3*x) / ((1 + 2*x)*(1 - 2*x - x^2)).
a(n) = 5*a(n-2) + 2*a(n-3) for n>3.
(End)
MATHEMATICA
LinearRecurrence[{0, 5, 2}, {0, 5, 3}, 30] (* Harvey P. Dale, May 03 2022 *)
PROG
(PARI) concat(0, Vec(x^2*(5 + 3*x) / ((1 + 2*x)*(1 - 2*x - x^2)) + O(x^35))) \\ Colin Barker, May 01 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Oct 14 2005
STATUS
approved