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A273053
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Numbers n such that 15*n^2 + 16 is a square.
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2
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0, 4, 32, 252, 1984, 15620, 122976, 968188, 7622528, 60012036, 472473760, 3719778044, 29285750592, 230566226692, 1815244062944, 14291386276860, 112515846151936, 885835382938628, 6974167217357088, 54907502355918076, 432285851629987520, 3403379310683982084
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OFFSET
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1,2
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LINKS
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FORMULA
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O.g.f.: 4*x^2/(1 - 8*x + x^2).
E.g.f.: 4*(1 + (4*sqrt(15)*sinh(sqrt(15)*x) - 15*cosh(sqrt(15)*x))*exp(4*x)/15). - Ilya Gutkovskiy, May 14 2016
a(n) = 8*a(n-1) - a(n-2) for n>2.
a(n) = -(2*((4-sqrt(15))^n*(4+sqrt(15))+(-4+sqrt(15))*(4+sqrt(15))^n))/sqrt(15). - Colin Barker, May 14 2016
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MAPLE
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a:=proc(n) option remember; if n=1 then 0 elif n=2 then 4 else 8*a(n-1) - a(n-2); fi; end: seq(a(n), n=1..30); # Wesley Ivan Hurt, May 14 2016
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MATHEMATICA
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LinearRecurrence[{8, -1}, {0, 4}, 30]
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PROG
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(Magma) [n: n in [0..2*10^7] |IsSquare(15*n^2+16)];
(PARI) concat(0, Vec(4*x^2/(1-8*x+x^2) + O(x^50))) \\ Colin Barker, May 14 2016
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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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