A145323 Numbers x such that there exists n in N : (x+1)^3-x^3=31*n^2.

22, 546817, 13288758862, 322943417329657, 7848170914656577702, 190726249245040733996497, 4635029301304809002926304542, 112640481889583219144074318995337, 2737388986245622090334485097298387382, 66524027031100626149725437690471091174177

Offset

1,1

Links

Table of n, a(n) for n=1..10.

Index entries for linear recurrences with constant coefficients, signature (24303,-24303,1).

Formula

a(n+2) = 24302*a(n+1)-a(n)+12150.

G.f.: x*(23*x^2-12151*x-22) / ((x-1)*(x^2-24302*x+1)). - Colin Barker, Oct 18 2014

Example

a(1)=22 because the first relation is : 23^3-22^3=31*7^2.

Mathematica

LinearRecurrence[{24303, -24303, 1}, {22, 546817, 13288758862}, 10] (* Paolo Xausa, Jan 17 2024 *)

Prog

(PARI) Vec(x*(23*x^2-12151*x-22) / ((x-1)*(x^2-24302*x+1)) + O(x^20)) \\ Colin Barker, Oct 18 2014

Crossrefs

Sequence in context: A362902 A238635 A013770 * A267492 A013816 A104789

Adjacent sequences: A145320 A145321 A145322 * A145324 A145325 A145326

Keyword

nonn,easy

Author

Richard Choulet, Oct 07 2008

Extensions

Editing and more terms from Colin Barker, Oct 18 2014

Status

approved