%I A051029
%S A051029 2,138,11468,951690,78978818,6554290188,543927106802,45139395574362,
%T A051029 3746025905565260,310875010766342202,25798879867700837522,
%U A051029 2140996154008403172108,177676881902829762447458
%N A051029 Ramanujan's b-series.
%C A051029 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 A051029 M. D. Hirschhorn, A Proof in the Spirit of Zeilberger of an Amazing Identity 
               of Ramanujan.
%D A051029 Jung Hun Han and Michael D. Hirschhorn, Another look at an amazing identity 
               of Ramanujan, Math. Magazine, 79, No. 2, 2006, 302-304.
%H A051029 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 A051029 G.f.: f(x)=(2-26x-12x^2)/(1-82x-82x^2+x^3).
%F A051029 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 A051029 g:=(2-26*x-12*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 A051029 Cf. A051028, A051030.
%Y A051029 Sequence in context: A139907 A087619 A157072 this_sequence A084560 A054681 
               A152509
%Y A051029 Adjacent sequences: A051026 A051027 A051028 this_sequence A051030 A051031 
               A051032
%K A051029 nonn
%O A051029 0,1
%A A051029 Eric Weisstein (eric(AT)weisstein.com)