%I A046184
%S A046184 1,9,121,1681,23409,326041,4541161,63250209,880961761,12270214441,
%T A046184 170902040409,2380358351281,33154114877521,461777249934009,
%U A046184 6431727384198601,89582406128846401,1247721958419651009
%N A046184 Indices of octagonal numbers which are also square.
%C A046184 a(n)=(A001835(n))^2. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 21 
               2006
%C A046184 Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.det), May 
               12 2009: The equation a(t)*(3*a(t)-2)=m*m is equivalent to the Pell 
               equation (3*a(t)-1)*(3*a(t)-1)-3*m*m=1.
%H A046184 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               OctagonalSquareNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A046184 Nearest integer to 1/6 * (2+sqrt(3))^(2n-1). - Ralf Stephan, Feb 24 2004
%F A046184 Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.det), May 
               12 2009: (Start)
%F A046184 With A=(2+sqrt(3))^2=7+4*sqrt(3) the equation x*x-3*m*m=1 has solutions
%F A046184 x(t)+sqrt(3)*m(t)=(2+sqrt(3))*A^t and the recurrences
%F A046184 x(t+2)=14*x(t+1)-x(t) with <x(t)> = 2,26,362,5042
%F A046184 m(t+2)=14*m(t+1)-m(t) with <m(t)> = 1,15,209,2911
%F A046184 a(t+2)=14*a(t+1)-a(t)-4 with <a(t)> = 1,9,121, as above
%F A046184 (End)
%p A046184 Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.det), May 
               12 2009: (Start)
%p A046184 for n from 1 to 10000 do m=sqrt(3*n*n-2*n): if (trunc(m)=m) then print(n,
               m):
%p A046184 end if: end do: (End)
%Y A046184 Cf. A028230, A036428.
%Y A046184 a(n) = A045899(n-1) + 1 = A051047(n+1) + 1 = A003697(2n-2).
%Y A046184 Sequence in context: A167722 A103930 A138978 this_sequence A084769 A050353 
               A112941
%Y A046184 Adjacent sequences: A046181 A046182 A046183 this_sequence A046185 A046186 
               A046187
%K A046184 nonn
%O A046184 1,2
%A A046184 Eric Weisstein (eric(AT)weisstein.com)