A275060 Numbers n such that there exists x in N : (x+1)^3 - x^3 = 61*n^2.

1, 973, 947701, 923059801, 899059298473, 875682833652901, 852914180918627101, 830737536531909143473, 809137507667898587115601, 788099101730996691941451901, 767607715948483110052387035973, 747649127234720818194333031585801

Offset: 1

Author

Colin Barker, Jul 15 2016

Keywords

• nonn
• easy

Examples

			973 is in the sequence because 973^2 = 946729 = ((4387+1)^3-4387^3)/61.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..300
• Index entries for linear recurrences with constant coefficients, signature (974,-1).

Crossrefs

Cf. A274972.

Programs

Mathematica

LinearRecurrence[{974,-1},{1,973}, 50] (* G. C. Greubel, Jul 15 2016 *)

PARI

Vec(x*(1-x)/(1-974*x+x^2) + O(x^20))

Formula

G.f.: x*(1-x) / (1-974*x+x^2).

a(n) = 974*a(n-1) - a(n-2) for n>2.

a(n) = ((487 + 36*sqrt(183))^(-n)*(2 - 9*sqrt(3/61) + (2+9*sqrt(3/61))* (487 + 36*sqrt(183))^(2*n)))/4.