Search: id:A046177
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%I A046177
%S A046177 1,1225,1413721,1631432881,1882672131025,2172602007770041,
%T A046177 2507180834294496361,2893284510173841030625,3338847817559778254844961,
%U A046177 3853027488179473932250054441,4446390382511295358038307980025
%N A046177 Square numbers which are also hexagonal numbers.
%C A046177 Also, odd square-triangular numbers (or bisection of A001110 = {0, 1, 
               36, 1225, 41616, 1413721, 48024900, 1631432881, ...} = Numbers that 
               are both triangular and square: a(n) = 34a(n-1) - a(n-2) + 2). - 
               Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 06 2007
%C A046177 Let be y^2=x*(2*x-1)=H_x (x>=1). The least both hexagonal and square 
               number which is greater than y^2 is given by the relation (24*x+17*y-6)^2 
               = H_{17*x+12*y-4}. [From Richard Choulet (richardchoulet(AT)yahoo.fr), 
               May 01 2009]
%H A046177 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HexagonalSquareNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A046177 Eric Weisstein, Link to a section of The World of Mathematics. <a href="http:/
               /mathworld.wolfram.com/SquareTriangularNumber.html">Square Triangular 
               Number</a>.
%F A046177 a(n) = A001110(2n-1). - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Nov 06 2007
%F A046177 a(n+1)=577*a(n)+36+204*(8*a(n)^2+a(n))^0.5 for n>=1 (a(0)=1) [From Richard 
               Choulet (richardchoulet(AT)yahoo.fr), May 01 2009]
%F A046177 a(n+2)=1154*a(n+1)-a(n)+72 for n>=0. [From Richard Choulet (richardchoulet(AT)yahoo.fr), 
               May 01 2009]
%Y A046177 Cf. A008844, A046176.
%Y A046177 Cf. A001110 = Numbers that are both triangular and square: a(n) = 34a(n-1) 
               - a(n-2) + 2.
%Y A046177 Sequence in context: A025405 A014795 A151657 this_sequence A031748 A031623 
               A031533
%Y A046177 Adjacent sequences: A046174 A046175 A046176 this_sequence A046178 A046179 
               A046180
%K A046177 nonn
%O A046177 1,2
%A A046177 Eric Weisstein (eric(AT)weisstein.com)

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