OFFSET
1,2
COMMENTS
The squares of the terms of A001651 are the squares of this sequence. - Bruno Berselli, Aug 12 2013
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = -13/2 - 3*(-1)^n/2 + 6*n.
a(n) = a(n-1) + a(n-2) - a(n-3).
G.f.: x*(8*x^2+3*x+1) / ((x-1)^2*(x+1)).
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(3)+3)*Pi/36 + log(2)/4 - sqrt(3)*log(26-15*sqrt(3))/36. - Amiram Eldar, Dec 28 2021
E.g.f.: 8 + ((12*x - 13)*exp(x) - 3*exp(-x))/2. - David Lovler, Sep 04 2022
MATHEMATICA
Select[Range[300], MemberQ[{1, 4}, Mod[#, 12]] &] (* Amiram Eldar, Dec 28 2021 *)
PROG
(PARI) Vec(x*(8*x^2+3*x+1)/((x-1)^2*(x+1)) + O(x^99))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Aug 12 2013
STATUS
approved