OFFSET
1,2
COMMENTS
a(1..4)=(1,4,6,11); a(n>4)=6*a(n-2)-a(n-4)+2. [From Ctibor O. Zizka, Nov 13 2009]
LINKS
F. T. Adams-Watters, SeqFan Discussion, Oct 2009
FORMULA
{k: 15+k*(k+1)/2 in A000290}.
Conjectures: (Start)
a(n)= +a(n-1) +6*a(n-4) -6*a(n-5) -a(n-8) +a(n-9).
G.f.: x*(-1-3*x-2*x^2-5*x^3-3*x^4+5*x^5+2*x^6+3*x^7+2*x^8)/((x-1) * (x^4+2*x^2-1) * (x^4-2*x^2-1)).
G.f.: ( 4 + (7+4*x+16*x^2+11*x^3)/(x^4-2*x^2-1) + 1/(x-1) + (-4-7*x-3*x^2-2*x^3)/(x^4+2*x^2-1) )/2. (End)
a(1..4) = (1,4,6,11); a(n) = 6*a(n-2) - a(n-4) + 2, for n>4. - Ctibor O. Zizka, Nov 13 2009
EXAMPLE
1*(1+1)/2+15 = 4^2. 4*(4+1)/2+15 = 5^2. 6*(6+1)/2+15 = 6^2. 11*(11+1)/2+15 = 9^2.
MATHEMATICA
Flatten[Position[Accumulate[Range[28000000]], _?(IntegerQ[Sqrt[#+15]]&)]] (* This program will take a long time to run. *) (* Harvey P. Dale, Jun 09 2014 *)
Join[{1, 4, 6}, Select[Range[0, 1000], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 15 &]] (* G. C. Greubel, Sep 03 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Oct 18 2009
EXTENSIONS
a(32)-a(37) from Donovan Johnson, Nov 01 2010
STATUS
approved