OFFSET
1,1
LINKS
F. T. Adams-Watters, SeqFan Discussion, Oct 2009
David A. Corneth, Conjectured formula for a(n)
FORMULA
{k: 28+k*(k+1)/2 in A000290}.
Conjectures: (Start)
a(n) = +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
G.f.: x*(-6-2*x-3*x^2+2*x^3+7*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)).
G.f.: ( 14 + 1/(x-1) + (14+29*x)/(x^2-2*x-1) + (-1-12*x)/(x^2+2*x-1) )/2. (End)
See also the Corneth link - David A. Corneth, Mar 18 2019
EXAMPLE
6, 8, 47, and 57 are terms:
6* (6+1)/2 + 28 = 7^2,
8* (8+1)/2 + 28 = 8^2,
47*(47+1)/2 + 28 = 34^2,
57*(57+1)/2 + 28 = 41^2.
MATHEMATICA
Join[{6, 8}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 28 &]] (* G. C. Greubel, Sep 03 2016 *)
PROG
(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 28), print1(n, ", ") ) ); }
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Oct 18 2009
EXTENSIONS
a(21)-a(30) from Amiram Eldar, Mar 18 2019
STATUS
approved