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A247375
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Numbers m such that floor(m/2) is a square.
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11
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0, 1, 2, 3, 8, 9, 18, 19, 32, 33, 50, 51, 72, 73, 98, 99, 128, 129, 162, 163, 200, 201, 242, 243, 288, 289, 338, 339, 392, 393, 450, 451, 512, 513, 578, 579, 648, 649, 722, 723, 800, 801, 882, 883, 968, 969, 1058, 1059, 1152, 1153, 1250, 1251, 1352, 1353
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OFFSET
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0,3
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COMMENTS
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Squares of the sequence are listed in A055792.
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LINKS
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FORMULA
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G.f.: x*( 1 + x - x^2 + 3*x^3 ) / ( (1 - x)^3*(1 + x)^2 ).
a(n) = 1 + ( 2*n*(n-1) + (2*n-3)*(-1)^n - 1 )/4.
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n >= 5. - Wesley Ivan Hurt, Dec 18 2020
Sum_{n>=1} 1/a(n) = Pi^2/12 + coth(Pi/sqrt(2))*Pi/(2*sqrt(2)) + 1/2. - Amiram Eldar, Sep 24 2022
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MATHEMATICA
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Select[Range[0, 1400], IntegerQ[Sqrt[Floor[#/2]]] &]
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 2, 3, 8}, 70] (* Harvey P. Dale, Oct 21 2021 *)
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PROG
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(Magma) [n: n in [0..1400] | IsSquare(Floor(n div 2))];
(Sage) [n for n in [0..1400] if is_square(floor(n/2))]
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CROSSREFS
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Cf. A130404 (numbers m such that floor(m/2) is a triangular number).
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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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