A263947 Positive integers n such that (n+57)^3 - n^3 is a square.

551, 13471, 67002512, 1560515752, 7745359676111, 180392503180711, 895348087775371352, 20853012581126608912, 103500448242912021166871, 2410566548172681237123151, 11964444815088795735075876992, 278656671814812593067838694872, 1383065891631134161140389210648831

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			551 is in the sequence because (551+57)^3 - 551^3 = 7581^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..394
• Index entries for linear recurrences with constant coefficients, signature (1,115598,-115598,-1,1).

Crossrefs

Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), A263946 (52), A263948 (61), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.

Programs

Mathematica

LinearRecurrence[{1, 115598, -115598, -1, 1}, {551, 13471, 67002512, 1560515752, 7745359676111}, 15] (* Paolo Xausa, Mar 05 2024 *)

PARI

Vec(19*x*(32*x^4+680*x^3-173397*x^2-680*x-29)/((x-1)*(x^2-340*x+1)*(x^2+340*x+1)) + O(x^20))

Formula

a(n) = a(n-1)+115598*a(n-2)-115598*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: 19*x*(32*x^4+680*x^3-173397*x^2-680*x-29) / ((x-1)*(x^2-340*x+1)*(x^2+340*x+1)).