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A081065
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Numbers n such that n^2 = (1/3)*(n+floor(sqrt(3)*n*floor(sqrt(3)*n))).
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2
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2, 24, 330, 4592, 63954, 890760, 12406682, 172802784, 2406832290, 33522849272, 466913057514, 6503259955920, 90578726325362, 1261598908599144, 17571805994062650, 244743685008277952, 3408839784121828674, 47479013292697323480, 661297346313640700042
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OFFSET
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1,1
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COMMENTS
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a(n)/2 gives indices of pentagonal numbers which are also triangular.
a(n) itself gives x-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2.
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LINKS
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FORMULA
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a(n) = 15*a(n-1) - 15*a(n-2) + a(n-3).
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MATHEMATICA
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LinearRecurrence[{15, -15, 1}, {2, 24, 330}, 20] (* Harvey P. Dale, Mar 14 2016 *)
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PROG
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(PARI) Vec(2*(1-3*x)/((1-x)*(1-14*x+x^2)) + O(x^40)) \\ Michel Marcus, Nov 17 2014
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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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STATUS
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approved
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