OFFSET
0,3
COMMENTS
It appears that for n>0, A143608(n) divides a(n).
The sequence a(n)/A143608(n) appears to generate A001541 interleaved with A001653. - R. J. Mathar, Jul 04 2012
It also appears that if p equals a prime of the form 8*r +/- 3 then a(p + 1) == 0 (mod p); and that if p is a prime in the form of 8*r +/- 1 then a(p - 1) == 0 (mod p), inherited from A143608.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
FORMULA
a(n) = A046090(n-1), for n>=1.
G.f.: x*(1-3*x)/((1-x)*(1-6*x+x^2)). - Bruno Berselli, May 15 2012
2*a(n)*(a(n)-1)+1 = A001653(n)^2 for n>0. - Bruno Berselli, Oct 23 2012
MATHEMATICA
m = -20;
n = -3;
c = 0;
list3 = Reap[While[c < 20, t = 6 n - m - 2; Sow[t]; m = n; n = t; c++]][[2, 1]]
LinearRecurrence[{7, -7, 1}, {0, 1, 4}, 30] (* Harvey P. Dale, May 11 2018 *)
PROG
(Magma) [n le 2 select n-1 else 6*Self(n-1)-Self(n-2)-2: n in [1..24]]; // Bruno Berselli, May 15 2012
(PARI) concat(0, Vec((1-3*x)/(1-x)/(1-6*x+x^2)+O(x^98))) \\ Charles R Greathouse IV, Jun 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kenneth J Ramsey, Apr 28 2012
STATUS
approved