OFFSET
1,1
COMMENTS
Positive integers y in the solutions to 2*x^2-100*y^2-4900*y-80850 = 0.
Numbers n such that 40425 + 2450*n + 50*n^2 is a square. - Harvey P. Dale, Oct 22 2016
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,6,-6,0,0,0,0,-1,1).
FORMULA
G.f.: x*(7+21*x+16*x^2+23*x^3+20*x^4+37*x^5+2*x^6-7*x^7-4*x^8-5*x^9-4*x^10-7*x^11-x^12) / ((1-x)*(1+2*x^3-x^6)*(1-2*x^3-x^6)).
EXAMPLE
7 is in the sequence because sum(k=7, 56, k^2) = 60025 = 245^2.
MATHEMATICA
Select[Range[3*10^6], IntegerQ[Sqrt[40425+2450#+50#^2]]&] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, -1, 1}, {7, 28, 44, 67, 87, 124, 168, 287, 379, 512, 628, 843, 1099}, 40] (* Harvey P. Dale, Oct 22 2016 *)
PROG
(PARI) Vec(x*(7+21*x+16*x^2+23*x^3+20*x^4+37*x^5+2*x^6-7*x^7-4*x^8-5*x^9-4*x^10-7*x^11-x^12) / ((1-x)*(1+2*x^3-x^6)*(1-2*x^3-x^6)) + O(x^40))
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Colin Barker, Feb 27 2016
STATUS
approved