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A125651
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Numbers k such that A125650(k) is a perfect square.
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5
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1, 3, 24, 147, 864, 5043, 29400, 171363, 998784, 5821347, 33929304, 197754483, 1152597600, 6717831123, 39154389144, 228208503747, 1330096633344, 7752371296323, 45184131144600, 263352415571283, 1534930362283104
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OFFSET
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1,2
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COMMENTS
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Corresponding numbers m such that m^2 = A125650(a(n)) are listed in A125652.
Disregarding the term 1, numbers k such that A071910(k) is a nonzero square; i.e., numbers k such that A000096(k) = k*(k+3)/2 is a nonzero square. - Rick L. Shepherd, Jul 13 2012
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LINKS
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FORMULA
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For n>1, a(n+2) = 6*a(n+1) - a(n) + 6.
For n>1, a(n) = ((3+2*sqrt(2))^(n-1) + (3-2*sqrt(2))^(n-1))*3/4 - 3/2.
For n>1, a(2)=3, a(3)=24, a(4)=147, a(n)=7*a(n-1)-7*a(n-2)+a(n-3) [From Harvey P. Dale, May 15 2011]
G.f.: (-1+x(4+(-10+x)x))/((-1+x)(1+(-6+x)x)) [From Harvey P. Dale, May 15 2011]
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EXAMPLE
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MATHEMATICA
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Join[{1}, LinearRecurrence[{7, -7, 1}, {3, 24, 147}, 35]] (* or *) CoefficientList[Series[(-1+x(4+(-10+x)x))/((-1+x)(1+(-6+x) x)), {x, 0, 35}], x] (* Harvey P. Dale, May 15 2011 *)
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PROG
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(Magma) I:=[1, 3, 24, 147]; [n le 4 select I[n] else 7*Self(n-1)-7*Self(n-2)+Self(n-3): n in [1..30]]; Vincenzo Librandi, May 21 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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