A263942 Positive integers n such that (n+4)^3 - n^3 is a square.

6, 28, 110, 416, 1558, 5820, 21726, 81088, 302630, 1129436, 4215118, 15731040, 58709046, 219105148, 817711550, 3051741056, 11389252678, 42505269660, 158631825966, 592022034208, 2209456310870, 8245803209276, 30773756526238, 114849222895680, 428623135056486

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			6 is in the sequence because (6+4)^3 - 6^3 = 28^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

Crossrefs

Cf. A263943 (21), A263944 (28), A263945 (39), 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[{5, -5, 1}, {6, 28, 110}, 30] (* Paolo Xausa, Mar 04 2024 *)

PARI

Vec(2*x*(x-3)/((x-1)*(x^2-4*x+1)) + O(x^40))

Formula

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

G.f.: 2*x*(x-3) / ((x-1)*(x^2-4*x+1)).