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A051028
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Ramanujan's a-series.
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3
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1, 135, 11161, 926271, 76869289, 6379224759, 529398785665, 43933719985479, 3645969360009049, 302571523160765631, 25109790452983538281, 2083810036074472911735, 172931123203728268135681
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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
| M. D. Hirschhorn, Ramanujan and Fermat's Last Theorem
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| G.f.: f(x)=(1+53x+9x^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:=(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
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CROSSREFS
| Cf. A051029, A051030.
Sequence in context: A195671 A004005 A143404 * A076011 A132054 A106175
Adjacent sequences: A051025 A051026 A051027 * A051029 A051030 A051031
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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