OFFSET
0,2
COMMENTS
Numbers k such that (4*k + 7)/3 is a square. - Bruno Berselli, Sep 11 2018
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Alexander Adamchuk, Apr 12 2006: (Start)
a(n) = 5 * Sum_{k=1..n} k^4 / Sum_{k=1..n} k^2, n > 0.
a(n) = a(n-1) + 6*n with a(0)=-1. - Vincenzo Librandi, Nov 18 2010
From G. C. Greubel, Sep 10 2018: (Start)
G.f.: (-1 + 8*x - x^2)/(1 - x)^3.
E.g.f.: (-1 + 6*x + 3*x^2)*exp(x). (End)
Sum_{n>=0} 1/a(n) = ( psi(1/2+sqrt(21)/6) - psi(1/2-sqrt(21)/6)) /sqrt(21) = -0.6286929... R. J. Mathar, Apr 24 2024
MATHEMATICA
Table[5*Sum[k^4, {k, 1, n}]/Sum[k^2, {k, 1, n}], {n, 1, 20}] (* Alexander Adamchuk, Apr 12 2006 *)
Table[3n^2+3n-1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {-1, 5, 17}, 40] (* Harvey P. Dale, Jan 18 2019 *)
PROG
(PARI) a(n)=3*n^2+3*n-1 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [3*n^2 + 3*n -1: n in [0..50]]; // G. C. Greubel, Sep 10 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Eric T. Lane (ERICLANE(AT)UTCVM.UTC.EDU)
STATUS
approved