A145212 Numbers x such that there exists n in N : (x+1)^3 - x^3 = 67*n^2.

146, 150922981, 155479346311338, 160173267776326886333, 165008898730338715685597026, 169990517382847468244368873843701, 175122531102470624411936031429357251258, 180409480316284222045549532749965177800150413

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..150

Index entries for linear recurrences with constant coefficients, signature (1030191,-1030191,1).

Formula

a(n+2) = 1030190*a(n+1)-a(n)+515094.

G.f.: x*(146+515095*x-147*x^2) / ((1-x)*(1-1030190*x+x^2)). - Colin Barker, Oct 18 2014, corrected Jul 13 2016

Example

The first relation is : 147^3-146^3=67*31^2.

Prog

(PARI) Vec(x*(146+515095*x-147*x^2)/((1-x)*(1-1030190*x+x^2)) + O(x^10)) \\ Colin Barker, Oct 18 2014, corrected Jul 13 2016
(PARI) isok(x) = issquare(((x+1)^3-x^3)/67) \\ Colin Barker, Jul 13 2016

Crossrefs

Sequence in context: A172877 A172911 A172933 * A195239 A122064 A320511

Adjacent sequences: A145209 A145210 A145211 * A145213 A145214 A145215

Keyword

nonn,easy

Author

Richard Choulet, Oct 04 2008

Extensions

Editing and additional term a(8) from Colin Barker, Oct 18 2014

a(2) to a(8) corrected by Colin Barker, Jul 13 2016

Status

approved