Search: id:A046174
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%I A046174
%S A046174 0,1,12,165,2296,31977,445380,6203341,86401392,1203416145,16761424636,
%T A046174 233456528757,3251629977960,45289363162681,630799454299572,
%U A046174 8785902997031325,122371842504138976,1704419892060914337
%N A046174 Indices of pentagonal numbers which are also triangular.
%H A046174 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PentagonalTriangularNumber.html">Link to a section of The World of 
               Mathematics.</a>
%F A046174 a(n) = 14*a(n-1) - a(n-2) - 2; g.f.: (1-3*x)/((1-x)*(1-14*x+x^2)) - Warut 
               Roonguthai (warut822(AT)yahoo.com) Jan 05 2001
%F A046174 a(n+1)=7*a(n)-1+2*(12*a(n)^2-4*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), 
               Sep 19 2007
%F A046174 a(n)=(1/6)-(1/12)*sqrt(3)*{[7-4*sqrt(3)]^n-[7+4*sqrt(3)]^n}-(1/12)*{[7+4*sqrt(3)]^n+[7-4*sqrt(3)]^n 
               }, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 25 2008]
%F A046174 a(n+1)=15*a(n)-15*a(n-1)+ a(n-2) a(1)=1,a(2)=12,a(3)=165 [From Sture 
               Sjoestedt (sture.sjostedt(AT)spray.se), May 29 2009]
%Y A046174 Cf. A014979, A046175.
%Y A046174 Cf. A046175 A014979 A001834.
%Y A046174 Sequence in context: A024221 A093152 A143583 this_sequence A055760 A056591 
               A099745
%Y A046174 Adjacent sequences: A046171 A046172 A046173 this_sequence A046175 A046176 
               A046177
%K A046174 nonn,easy
%O A046174 0,3
%A A046174 Eric Weisstein (eric(AT)weisstein.com)

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