%I A046195
%S A046195 1,6,49,961,8214,70225,1385329,11844150,101263969,1997643025,
%T A046195 17079255654,146022572641,2880599856289,24628274808486,
%U A046195 210564448483921,4153822995125281,35513955194580726
%N A046195 Indices of heptagonal numbers (A000566) which are also square.
%H A046195 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeptagonalSquareNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A046195 Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.de), May 
               01 2009: (Start)
%F A046195 Pell equations: r^2-10*s^2=1 with solution (19,6)
%F A046195 (10*n-3)^2-10*(2*m)^2=9; basic solutions: (7,-2); (7,+2)((57,18);
%F A046195 with x=10*n-3; y=2*m; A=(19+6*sqrt(10))^2; B=(19-6*sqrt(10))^2 one get
%F A046195 x(3*k)+sqrt(10)*y(3*k)=(7-2*sqrt(10))*A^k;
%F A046195 x(3*k+1)+sqrt(10)*y(3*k+1)=(7+2*sqrt(10))*A^k;
%F A046195 x(3*k+2)+sqrt(10)*y(3*k+2)=(57+18*sqrt(10))*A^k;
%F A046195 with the eigenwerten A=721+228*sqrt(10); B=721-228*sqrt(10)
%F A046195 one get the recurences with 1442=4*19*19-2
%F A046195 x(k+6)=1442*x(k+3)-x(k); y(k+6)=1442*y(k+3)-y(k);
%F A046195 m(k+6)=1442*m(k+3)-m(k); n(k+6)=1442*n(k+3)-n(k)-432;
%F A046195 and the explicit formulas
%F A046195 x(3*k+1)=(7*(A^k+B^k)+2*sqrt(10)*(A^k-B^k))/2;
%F A046195 x(3*k+2)=(57*(A^k+B^k)+18*sqrt(10)*(A^k-B^k))/2;
%F A046195 x(3*k)=(7*(A^k+B^k)-2*sqrt(10)*(A^k-B^k))/2;
%F A046195 y(3*k+1)=(7*(A^k-B^k)/sqrt(10)+2*(A^k+B^k)/2;
%F A046195 y(3*k+2)=(57*(A^k-B^k)/sqrt(10)+18*(A^k+B^k))/2;
%F A046195 y(3*k)=(7*(A^k-B^k)/sqrt(10)-2*(A^k+B^k))/2;
%F A046195 n(k)=(x(k)+3)/10; m(k)=y(k)/2;
%F A046195 (End)
%p A046195 Contribution from Weisenhorn Paul (paulweisenhorn(AT)online.de), May 
               01 2009: (Start)
%p A046195 for n from 1 to 10000 do m:=sqrt((5*n^2-3*n)/2):
%p A046195 if (trunc(m)=m) then print(n,m): end if: end do:
%p A046195 (End)
%Y A046195 Cf. A000566, A036254, A046196.
%Y A046195 Sequence in context: A055847 A143165 A008786 this_sequence A024268 A062801 
               A035290
%Y A046195 Adjacent sequences: A046192 A046193 A046194 this_sequence A046196 A046197 
               A046198
%K A046195 nonn
%O A046195 1,2
%A A046195 Eric Weisstein (eric(AT)weisstein.com)