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A077288
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First member of the Diophantine pair (m,k) that satisfies 6(m^2+m)=k^2+k: a(n)=m.
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6
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0, 1, 3, 14, 34, 143, 341, 1420, 3380, 14061, 33463, 139194, 331254, 1377883, 3279081, 13639640, 32459560, 135018521, 321316523, 1336545574, 3180705674
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also nonnegative m such that 24*m^2 + 24*m + 1 is a square. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Apr 02 2005
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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 A072256. Then a(2n+2)=2*a(2n+1)-a(2n)+b(n+1), a(2n+3)=2*a(2n+2)-a(2n+1)+b(n+2), with a(0)=0, a(1)=1; g.f.: A(x)=x*(1+x)^2/((1-x)*(1-10x^2+x^4).
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EXAMPLE
| a(3)=(2*3)-1+9=14, a(4)=(2*14)-3+9=34 etc.
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CROSSREFS
| The k values are in A077291
Cf. A077289, A077290, A077291.
Cf. A053141.
Sequence in context: A081269 A140064 A064226 * A094627 A009394 A076533
Adjacent sequences: A077285 A077286 A077287 * A077289 A077290 A077291
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KEYWORD
| easy,nonn
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AUTHOR
| Bruce Corrigan (scentman(AT)myfamily.com), Nov 03 2002
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