Search: id:A051030
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%I A051030
%S A051030 2,172,14258,1183258,98196140,8149096378,676276803218,56122825570732,
%T A051030 4657518245567522,386517891556533610,32076327480946722092,
%U A051030 2661948663027021400042,220909662703761829481378
%N A051030 Ramanujan's c-series.
%C A051030 The "amazing" identity of Ramanujan is a(n)^3 + b(n)^3 = c(n)^3 + (-1)^n, 
               where a(n)=A051028(n), b(n)=A051029(n) and c(n)=A051030(n). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
%D A051030 M. D. Hirschhorn, A Proof in the Spirit of Zeilberger of an Amazing Identity 
               of Ramanujan.
%D A051030 Jung Hun Han and Michael D. Hirschhorn, Another look at an amazing identity 
               of Ramanujan, Math. Magazine, 79, No. 2, 2006, 302-304.
%H A051030 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RamanujansSumIdentity.html">Link to a section of The World of Mathematics.</
               a>
%F A051030 G.f.: f(x)=(2+8x-10x^2)/(1-82x-82x^2+x^3).
%F A051030 X(n+1)=AX(n), where X(n)=transpose(A051028(n), A051029(n), A051030(n)) 
               and A = matrix (3,3,[63,104,-68; 64,104,-67; 80,131,-85)]). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2006
%p A051030 g:=(2+8*x-10*x^2)/(1-82*x-82*x^2+x^3): gser:=series(g,x=0,20): seq(coeff(gser,
               x,n),n=0..12); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 
               2006
%Y A051030 Cf. A051028, A051029.
%Y A051030 Sequence in context: A157316 A163970 A007760 this_sequence A139935 A103427 
               A139942
%Y A051030 Adjacent sequences: A051027 A051028 A051029 this_sequence A051031 A051032 
               A051033
%K A051030 nonn
%O A051030 0,1
%A A051030 Eric Weisstein (eric(AT)weisstein.com)

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