A145210 Numbers n such that there exists x in N : (x+1)^3-x^3=67*n^2.

31, 31935859, 32900002583179, 33893253661133238151, 34916490989129950608195511, 35970619852057890563395800238939, 37056572865356601788515589497544372899, 38175310800125746976658817253911841716581871, 39327823433144486705018790345018924628507933312591

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..170

Index entries for linear recurrences with constant coefficients, signature (1030190,-1).

Formula

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

a(n) = A145207(n)/4489. - Colin Barker, Oct 19 2014

G.f.: -31*x*(x-1) / (x^2-1030190*x+1). - Colin Barker, Oct 19 2014

a(n) = A145205(n)/134. - Hugo Pfoertner, Apr 08 2024

Example

a(1)=31 because the first relation is : 147^3-146^3=67*31^2.

Mathematica

CoefficientList[Series[31 (1 - x)/(x^2 - 1030190 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 19 2014 *)
LinearRecurrence[{1030190, -1}, {31, 31935859}, 10] (* Harvey P. Dale, Aug 11 2021 *)

Prog

(PARI) Vec(-31*x*(x-1)/(x^2-1030190*x+1) + O(x^20)) \\ Colin Barker, Oct 19 2014
(Magma) I:=[31, 31935859]; [n le 2 select I[n] else 1030190*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, Oct 19 2014

Crossrefs

Cf. A145205, A145207.

Sequence in context: A342118 A216791 A324268 * A091308 A023927 A345676

Adjacent sequences: A145207 A145208 A145209 * A145211 A145212 A145213

Keyword

easy,nonn

Author

Richard Choulet, Oct 04 2008

Extensions

Editing and more terms from Colin Barker, Oct 19 2014

Status

approved