A263945 Positive integers n such that (n+39)^3 - n^3 is a square.

26, 871, 59930, 1155895, 77814386, 1500376111, 101003038370, 1947487061455, 131101866015146, 2527836705417751, 170170121084646410, 3281130096145204615, 220880686066005050306, 4258904336959770197791, 286702960343553470676050, 5528054548243685571553375

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			26 is in the sequence because (26+39)^3 - 26^3 = 507^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..642
• Index entries for linear recurrences with constant coefficients, signature (1,1298,-1298,-1,1).

Crossrefs

Cf. A263942 (4), A263943 (21), A263944 (28), A263946 (52), A263947 (57), A263948 (61), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.

Programs

Mathematica

LinearRecurrence[{1,1298,-1298,-1,1},{26,871,59930,1155895,77814386},20] (* Harvey P. Dale, Mar 25 2020 *)

PARI

Vec(13*x*(5*x^4+65*x^3-1947*x^2-65*x-2)/((x-1)*(x^2-36*x-1)*(x^2+36*x-1)) + O(x^30))

Formula

a(n) = a(n-1)+1298*a(n-2)-1298*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: 13*x*(5*x^4+65*x^3-1947*x^2-65*x-2) / ((x-1)*(x^2-36*x-1)*(x^2+36*x-1)).