|
%I #17 May 20 2021 13:15:59
%S 0,335,815,772320,1877280,1777881455,4321498895,4092682338240,
%T 9948088580160,9421352964748175,22900495590030575,
%U 21687950432167961760,52716930900161804640,49925652473497683224495,121354352031676884251855
%N Nonnegative numbers n such that 23*n^2 + 23*n + 1 = j^2 = a square.
%C 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
%C In terms of indices of triangular numbers: A000217(n) = 4*A000217[(j-1)/2]/23. - _R. J. Mathar_, Dec 05 2007
%H Harvey P. Dale, <a href="/A105099/b105099.txt">Table of n, a(n) for n = 1..595</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,2302,-2302,-1,1).
%F 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
%F 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
%t LinearRecurrence[{1,2302,-2302,-1,1},{0,335,815,772320,1877280},20] (* _Harvey P. Dale_, May 20 2021 *)
%K nonn,easy
%O 1,2
%A _Pierre CAMI_, Apr 07 2005
%E More terms from _Max Alekseyev_, Apr 09 2005
%E More terms from _R. J. Mathar_, Dec 05 2007
|
