A105099 Nonnegative numbers n such that 23*n^2 + 23*n + 1 = j^2 = a square.

0, 335, 815, 772320, 1877280, 1777881455, 4321498895, 4092682338240, 9948088580160, 9421352964748175, 22900495590030575, 21687950432167961760, 52716930900161804640, 49925652473497683224495, 121354352031676884251855

Offset

1,2

Comments

a(5)=2649601*(2*a(1)+1)-1-a(4), a(6)=2649601*(2*a(2)+1)-1-a(3), a(7)=2649601*(2*a(3)+1)-1-a(2), a(8)=2649601*(2*a(4)+1)-1-a(1), a(9)=2649601*(2*a(5)+1)-1-a(1), a(10)=2649601*(2*a(6)+1)-1-a(2), a(11)=2649601*(2*a(7)+1)-1-a(3), a(12)=2649601*(2*a(8)+1)-1-a(4), a(13)=2649601*(2*a(9)+1)-1-a(1), a(14)=2649601*(2*a(10)+1)-1-a(1). This is a strange recurrence - does it continue ? Remark : 2649601 = 23*24*25*192+1

In terms of indices of triangular numbers: A000217(n) = 4*A000217[(j-1)/2]/23. - R. J. Mathar, Dec 05 2007

Links

Harvey P. Dale, Table of n, a(n) for n = 1..595

Index entries for linear recurrences with constant coefficients, signature (1,2302,-2302,-1,1).

Formula

Union of two sequences defined by the recurrence a(n+1)=2302*a(n)-a(n-1)+1150 a(0)=0, a(1)=335, a(2)=772320, ... a(0)=0, a(1)=815, a(2)=1877280, ... - Max Alekseyev, Apr 09 2005

O.g.f.: -5*(67*x^2+96*x+67)*x^2/((x^2+48*x+1)*(x^2-48*x+1)*(-1+x)). - R. J. Mathar, Dec 05 2007

Mathematica

LinearRecurrence[{1, 2302, -2302, -1, 1}, {0, 335, 815, 772320, 1877280}, 20] (* Harvey P. Dale, May 20 2021 *)

Crossrefs

Sequence in context: A046015 A184076 A253227 * A038648 A224533 A253346

Adjacent sequences: A105096 A105097 A105098 * A105100 A105101 A105102

Keyword

nonn,easy

Author

Pierre CAMI, Apr 07 2005

Extensions

More terms from Max Alekseyev, Apr 09 2005

More terms from R. J. Mathar, Dec 05 2007

Status

approved