OFFSET
0,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..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
G.f.: -31*(1 + 29*x + 32*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 21 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(31))*Pi/sqrt(31) + 1)/62.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(31))*Pi/sqrt(31) + 1)/62. (End)
From Elmo R. Oliveira, Jan 13 2025: (Start)
E.g.f.: 31*exp(x)*(31*x^2 + 31*x + 1).
a(n) = 31*A247155(n). (End)
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {31, 992, 3875}, 50] (* Vincenzo Librandi, Feb 19 2012 *)
961 Range[0, 40]^2+31 (* or *) CoefficientList[Series[-((31 (1+29 x+32 x^2))/(-1+x)^3), {x, 0, 40}], x] (* Harvey P. Dale, Jul 31 2021 *)
PROG
(Magma) I:=[31, 992, 3875]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 19 2012
(PARI) for(n=0, 40, print1(961*n^2 + 31", ")); \\ Vincenzo Librandi, Feb 19 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 24 2009
EXTENSIONS
Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009
STATUS
approved