Search: id:A014979
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%I A014979
%S A014979 0,1,210,40755,7906276,1533776805,297544793910,57722156241751,
%T A014979 11197800766105800,2172315626468283465,421418033734080886426,
%U A014979 81752926228785223683195,15859646270350599313653420
%N A014979 Numbers that are both triangular and pentagonal.
%D A014979 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 210, p. 61, Ellipses, 
               Paris 2008.
%D A014979 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 
               256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see 
               vol. 2, p. 22.
%H A014979 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 A014979 a(n) = 194a(n-1) - a(n-2) + 16; g.f.: (1+15*x)/((1-x)*(1-194*x+x^2)).
%F A014979 a(n)=((((1+sqrt(3))^(4n-1)-(1-sqrt(3))^(4n-1))/(2^(2n+1)*sqrt(3)))^2)/
               2-1/8. - John Sillcox (johnsillcox(AT)hotmail.com), Sep 01 2003
%F A014979 a(n)=A076139(2n+1). - Michael Somos, May 30 2005
%F A014979 a(n+1)=97*a(n)+8+7*(192*a(n)^2+32*a(n)+1)^0.5 - Richard Choulet (richardchoulet(AT)yahoo.fr), 
               Sep 19 2007
%e A014979 a(2)=40755 which is 285(285-1)/2 = 165(3*165-1)/2.
%o A014979 (PARI) a(n)=subst((-8+15*poltchebi(2*n+1)-poltchebi(2*n))/96,x, 7) - 
               Michael Somos, May 30 2005
%Y A014979 Cf. A046174, A046175.
%Y A014979 Sequence in context: A140904 A092711 A089514 this_sequence A134236 A136350 
               A068297
%Y A014979 Adjacent sequences: A014976 A014977 A014978 this_sequence A014980 A014981 
               A014982
%K A014979 nonn,easy
%O A014979 1,3
%A A014979 Glenn Johnston (glennj(AT)sonic.net)
%E A014979 Corrected and extended by Warut Roonguthai (warut822(AT)yahoo.com)
%E A014979 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 24 2006

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