A263944 Positive integers n such that (n+28)^3 - n^3 is a square.

28, 189, 959, 4648, 22323, 107009, 512764, 2456853, 11771543, 56400904, 270233019, 1294764233, 6203588188, 29723176749, 142412295599, 682338301288, 3269279210883, 15664057753169, 75051009555004, 359590990021893, 1722903940554503, 8254928712750664

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			189 is in the sequence because (189+28)^3 - 189^3 = 1862^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-6,1).

Crossrefs

Cf. A263942 (4), A263943 (21), 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[{6,-6,1},{28,189,959},30] (* Harvey P. Dale, Dec 14 2016 *)

PARI

Vec(7*x*(x-4)*(x+1)/((x-1)*(x^2-5*x+1)) + O(x^40))

Formula

a(n) = 6*a(n-1)-6*a(n-2)+a(n-3) for n>3.

G.f.: 7*x*(x-4)*(x+1) / ((x-1)*(x^2-5*x+1)).

a(n) = 7*(-2+(2^(-1-n)*((5-sqrt(21))^n*(-7+sqrt(21))+(5+sqrt(21))^n*(7+sqrt(21))))/sqrt(21)). - Colin Barker, Mar 05 2016