Search: id:A051028
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%I A051028
%S A051028 1,135,11161,926271,76869289,6379224759,529398785665,43933719985479,
%T A051028 3645969360009049,302571523160765631,25109790452983538281,
%U A051028 2083810036074472911735,172931123203728268135681
%N A051028 Ramanujan's a-series.
%C A051028 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 A051028 M. D. Hirschhorn, A Proof in the Spirit of Zeilberger of an Amazing Identity 
               of Ramanujan.
%D A051028 Jung Hun Han and Michael D. Hirschhorn, Another look at an amazing identity 
               of Ramanujan, Math. Magazine, 79, No. 2, 2006, 302-304.
%H A051028 M. D. Hirschhorn, <a href="http://www.austms.org.au/Publ/Gazette/2004/
               Sept04/hirschhorn.pdf">Ramanujan and Fermat's Last Theorem</a>
%H A051028 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 A051028 G.f.: f(x)=(1+53x+9x^2)/(1-82x-82x^2+x^3).
%F A051028 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 A051028 g:=(1+53*x+9*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 A051028 Cf. A051029, A051030.
%Y A051028 Sequence in context: A061073 A004005 A143404 this_sequence A076011 A132054 
               A106175
%Y A051028 Adjacent sequences: A051025 A051026 A051027 this_sequence A051029 A051030 
               A051031
%K A051028 nonn
%O A051028 0,2
%A A051028 Eric Weisstein (eric(AT)weisstein.com)

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