Search: id:A046178
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%I A046178
%S A046178 1,165,31977,6203341,1203416145,233456528757,45289363162681,
%T A046178 8785902997031325,1704419892060914337,330648673156820350021,
%U A046178 64144138172531086989705
%N A046178 Indices of pentagonal numbers which are also hexagonal.
%C A046178 The reason is that we obtain the same Diophantine equation with various 
               parameters is the following: the number which is written 361 in base 
               4*A046179(n)-2 is the square of 6*A046178(n)-1. That is, 361 in base 
               110770 is 3*110770^2+6*110770+1=36810643321 i.e. the square of 191861 
               if we consider the third terms of A046179 and A046178 which are 27693 
               and 31977 respectively. - Richard Choulet (richardchoulet(AT)yahoo.fr), 
               Oct 03 2007
%H A046178 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HexagonalPentagonalNumber.html">Link to a section of The World of 
               Mathematics.</a>
%F A046178 a(n) = 194*a(n-1) - a(n-2) - 32; g.f.: (1-30*x-3*x^2)/((1-x)*(1-194*x+x^2)) 
               - Warut Roonguthai (warut822(AT)yahoo.com) Jan 08 2001
%F A046178 a(n+1)=97*a(n)-16+28*(12*a(n)^2-4*a(n)+1)^0.5 - R. Choulet (richardchoulet(AT)yahoo.fr), 
               Oct 09 2007
%F A046178 a(n)=(1/6)+(5/12)*[97-56*sqrt(3)]^n+(5/12)*[97+56*sqrt(3)]^n-(1/4)*[97-56*sqrt(3)]^n*sqrt(3) 
               +(1/4)*sqrt(3)*[97+56*sqrt(3)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), 
               Sep 26 2008]
%Y A046178 Cf. A046179, A046180.
%Y A046178 Cf. A046179 A046180.
%Y A046178 Sequence in context: A071576 A140912 A132055 this_sequence A015982 A065210 
               A038007
%Y A046178 Adjacent sequences: A046175 A046176 A046177 this_sequence A046179 A046180 
               A046181
%K A046178 nonn,easy
%O A046178 1,2
%A A046178 Eric Weisstein (eric(AT)weisstein.com)

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