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A287057 a(n) = 2*n^2 + n - (n+1) mod 2.

%I A287057 #46 Sep 08 2022 08:46:19
%S A287057 3,9,21,35,55,77,105,135,171,209,253,299,351,405,465,527,595,665,741,
%T A287057 819,903,989,1081,1175,1275,1377,1485,1595,1711,1829,1953,2079,2211,
%U A287057 2345,2485,2627,2775,2925,3081,3239,3403,3569,3741,3915,4095
%N A287057 a(n) = 2*n^2 + n - (n+1) mod 2.
%C A287057 Let r(n) = (a(n)-1)/a(n) if n mod 2 = 1, (a(n)+1)/a(n) otherwise; then Product_{n>=1} r(n) = (2/3) * (10/9) * (20/21) * (36/35) * (54/55) * (78/77) * (104/105) * (136/135) * ... = agm(1,sqrt(2))^2/2 = 0.7177700110461299978211932237.
%H A287057 Vincenzo Librandi, <a href="/A287057/b287057.txt">Table of n, a(n) for n = 1..1000</a>
%H A287057 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A287057 G.f.: x*(3+3*x+3*x^2-x^3)/((1+x)*(1-x)^3). - _Robert Israel_, Aug 11 2017
%p A287057 seq(2*n^2 + n - ((n+1) mod 2), n = 1 .. 30); # _Robert Israel_, Aug 11 2017
%t A287057 a[n_] := 2 n^2 + n - Mod[n + 1, 2]; Array[a, 50] (* _Robert G. Wilson v_, Aug 10 2017 *)
%o A287057 (PARI) {for(n=1,100,print1(2*n^2+n-(n+1)%2", "))}
%o A287057 (Magma) [2*n^2+n-(n+1) mod 2: n in [1..60]]; // _Vincenzo Librandi_, Aug 12 2017
%Y A287057 Cf. A033566, A033567.
%K A287057 nonn
%O A287057 1,1
%A A287057 _Dimitris Valianatos_, Jun 24 2017