A263948 Positive integers n such that (n+61)^3 - n^3 is a square.

244, 267607, 260678620, 253900737919, 247299058084132, 240869028673236295, 234606186628674096844, 228506184907299897119407, 222564789493523471120235220, 216777876460506953571212014519, 211141429107744279254889381935932, 205651535173066467487308686793612895

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			244 is in the sequence because (244+61)^3 - 244^3 = 3721^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..334
• Index entries for linear recurrences with constant coefficients, signature (975,-975,1).

Crossrefs

Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), A263946 (52), A263947 (57), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.

Programs

Mathematica

LinearRecurrence[{975, -975, 1}, {244, 267607, 260678620}, 15] (* Paolo Xausa, Mar 05 2024 *)

PARI

Vec(61*x*(5*x^2-487*x-4)/((x-1)*(x^2-974*x+1)) + O(x^15))

Formula

a(n) = 975*a(n-1)-975*a(n-2)+a(n-3) for n>3.

G.f.: 61*x*(5*x^2-487*x-4) / ((x-1)*(x^2-974*x+1)).