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A077259
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First member of the Diophantine pair (m,k) that satisfies 5*(m^2+m)=k^2+k; a(n)=m.
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4
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0, 2, 6, 44, 116, 798, 2090, 14328, 37512, 257114, 673134, 4613732
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Conjecture: a(0)=0, a(1)=2, a(2)=6, a(3)=44, a(n)=18a(n-2)-a(n-4)+8 [From Robert Phillips (bobanne(AT)bellsouth.net), Sep 01 2008]
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REFERENCES
| Mohammad K. Azarian, Diophantine Pair, Problem B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278. Solution appeared in Vol. 38, No. 2, May 2000, pp. 183-184.
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FORMULA
| Let b(n) be A007805(n). Then with a(0)=0, a(1)=2, a(2n+2)=2*a(2n+1)-a(2n)+2*b(n), a(2n+3)=2*a(2n+2)-a(2n+1)+2*b(n+1).
a(n) = (A000045(A007310(n+1))-1)/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 02 2002. [Corrected by R. J. Mathar, Sep 16 2009]
a(0)=0, a(1)=2, a(n+2)=4+9a(n)+2Sqrt(1+20a(n)+20a(n)^2) - Herbert Kociemba (kociemba(AT)t-online.de), May 12 2008
G.f.:(-2*x*(x+1)^2)/((x-1)*(x^2-4*x-1)*(x^2+4*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
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EXAMPLE
| a(3)=(2*6)-2+(2*17)=12-2+34=44
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CROSSREFS
| Cf. A007805, A077260, A077261, A077262.
Cf. A053141.
Sequence in context: A066863 A135815 A055564 * A136589 A077048 A120594
Adjacent sequences: A077256 A077257 A077258 * A077260 A077261 A077262
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KEYWORD
| easy,nonn
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AUTHOR
| Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002
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