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A051030
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Ramanujan's c-series.
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3
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2, 172, 14258, 1183258, 98196140, 8149096378, 676276803218, 56122825570732, 4657518245567522, 386517891556533610, 32076327480946722092, 2661948663027021400042, 220909662703761829481378
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
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REFERENCES
| 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.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| G.f.: f(x)=(2+8x-10x^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
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MAPLE
| 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
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CROSSREFS
| Cf. A051028, A051029.
Sequence in context: A005020 A157316 A007760 * A139935 A172231 A193638
Adjacent sequences: A051027 A051028 A051029 * A051031 A051032 A051033
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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