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A247375 Numbers m such that floor(m/2) is a square.

%I A247375 #45 Sep 24 2022 05:47:30
%S A247375 0,1,2,3,8,9,18,19,32,33,50,51,72,73,98,99,128,129,162,163,200,201,
%T A247375 242,243,288,289,338,339,392,393,450,451,512,513,578,579,648,649,722,
%U A247375 723,800,801,882,883,968,969,1058,1059,1152,1153,1250,1251,1352,1353
%N A247375 Numbers m such that floor(m/2) is a square.
%C A247375 Union of A001105 and A058331.
%C A247375 Squares of the sequence are listed in A055792.
%H A247375 Jens Kruse Andersen, <a href="/A247375/b247375.txt">Table of n, a(n) for n = 0..10000</a>
%H A247375 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A247375 G.f.: x*( 1 + x - x^2 + 3*x^3 ) / ( (1 - x)^3*(1 + x)^2 ).
%F A247375 a(n) = 1 + ( 2*n*(n-1) + (2*n-3)*(-1)^n - 1 )/4.
%F A247375 a(n+1) = 1 + A213037(n).
%F A247375 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
%F A247375 Sum_{n>=1} 1/a(n) = Pi^2/12 + coth(Pi/sqrt(2))*Pi/(2*sqrt(2)) + 1/2. - _Amiram Eldar_, Sep 24 2022
%t A247375 Select[Range[0, 1400], IntegerQ[Sqrt[Floor[#/2]]] &]
%t A247375 LinearRecurrence[{1,2,-2,-1,1},{0,1,2,3,8},70] (* _Harvey P. Dale_, Oct 21 2021 *)
%o A247375 (Magma) [n: n in [0..1400] | IsSquare(Floor(n div 2))];
%o A247375 (Sage) [n for n in [0..1400] if is_square(floor(n/2))]
%Y A247375 Cf. A001105, A055792, A058331, A213037.
%Y A247375 Cf. A130404 (numbers m such that floor(m/2) is a triangular number).
%K A247375 nonn,easy
%O A247375 0,3
%A A247375 _Bruno Berselli_, Sep 15 2014