A263949 Positive integers n such that (n+84)^3 - n^3 is a square.

28, 476, 1106, 8218, 18256, 131600, 291578, 2097970, 4647580, 33436508, 74070290, 532886746, 1180477648, 8492752016, 18813572666, 135351146098, 299836685596, 2157125586140, 4778573397458, 34378658232730, 76157337674320, 547901406138128, 1213738829392250

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			28 is in the sequence because (28+84)^3 - 28^3 = 1176^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,16,-16,-1,1).

Crossrefs

Cf. A263942 (4), A263943 (21), A263944 (28), A263945 (39), A263946 (52), A263947 (57), A263948 (61) where the parenthesized number is k in the expression (n+k)^3 - n^3.

Programs

Mathematica

LinearRecurrence[{1, 16, -16, -1, 1}, {28, 476, 1106, 8218, 18256}, 30] (* Paolo Xausa, Mar 05 2024 *)

PARI

Vec(14*x*(x^4+4*x^3-13*x^2-32*x-2)/((x-1)*(x^4-16*x^2+1)) + O(x^40))

Formula

a(n) = a(n-1)+16*a(n-2)-16*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: 14*x*(x^4+4*x^3-13*x^2-32*x-2) / ((x-1)*(x^4-16*x^2+1)).