OFFSET
1,1
COMMENTS
Sequence found by reading the line from 12, in the direction 12, 60,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f: 4*x*(3+6*x-x^2)/(1-x)^3.
From Amiram Eldar, Mar 05 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/8.
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi-2)/16. (End)
MATHEMATICA
16Range[60]^2-4 (* Harvey P. Dale, Mar 18 2011 *)
PROG
(Magma) I:=[12, 60, 140]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]];
(PARI) a(n) = 16*n^2 - 4.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 19 2009
STATUS
approved