0,1

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

M. D. Hirschhorn, A Proof in the Spirit of Zeilberger of an Amazing Identity of Ramanujan.

Jung Hun Han and Michael D. Hirschhorn, Another look at an amazing identity of Ramanujan, Math. Magazine, 79, No. 2, 2006, 302-304.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

G.f.: f(x)=(2-26x-12x^2)/(1-82x-82x^2+x^3).

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

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

Cf. A051028, A051030.

Sequence in context: A000662 A139907 A087619 this_sequence A084560 A054681 A094482

Adjacent sequences: A051026 A051027 A051028 this_sequence A051030 A051031 A051032

nonn

Eric Weisstein (eric(AT)weisstein.com)