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
Examples
The first relation is : 147^3-146^3=67*31^2.
Links
- Colin Barker, Table of n, a(n) for n = 1..150
- Index entries for linear recurrences with constant coefficients, signature (1030191,-1030191,1).
Programs
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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
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PARI
isok(x) = issquare(((x+1)^3-x^3)/67) \\ Colin Barker, Jul 13 2016
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
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