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A286264 a(n) = 2*(ceiling((n^2)/2)+1) - 1.

%I A286264 #48 Jul 26 2024 08:57:56
%S A286264 3,5,11,17,27,37,51,65,83,101,123,145,171,197,227,257,291,325,363,401,
%T A286264 443,485,531,577,627,677,731,785,843,901,963,1025,1091,1157,1227,1297,
%U A286264 1371,1445,1523,1601,1683,1765,1851,1937,2027,2117,2211,2305,2403,2501
%N A286264 a(n) = 2*(ceiling((n^2)/2)+1) - 1.
%H A286264 Colin Barker, <a href="/A286264/b286264.txt">Table of n, a(n) for n = 1..1000</a>
%H A286264 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A286264 a(n) > n^2.
%F A286264 From _Colin Barker_, May 05 2017: (Start)
%F A286264 G.f.: x*(3 - x + x^2 + x^3) / ((1 - x)^3*(1 + x)).
%F A286264 a(n) = 3/2 - (-1)^n/2 + n^2.
%F A286264 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4. (End)
%F A286264 Sum_{n>=1} 1/a(n) = Pi*coth(Pi/2)/4 + Pi*tanh(Pi/sqrt(2))/(4*sqrt(2)) - 1/2. - _Amiram Eldar_, Jul 26 2024
%e A286264 n=2: (1*3*5*7)/(2*4*6*8) = (1*1*5*7)/(2*4*2*8) => a(2) = 5 = A151800(2^2).
%e A286264 n=3: (1*3*5*7*9*11*13*15*17)/(2*4*6*8*10*12*14*16*18) = (1*1*1*1*1*11*13*15*17)/(2*4*2*8*2*12*2*16*2) => a(3) = 11 = A151800(3^2).
%p A286264 A286264:=n->3/2 - (-1)^n/2 + n^2: seq(A286264(n), n=1..100); # _Wesley Ivan Hurt_, May 05 2017
%t A286264 Table[2 (Ceiling[n^2/2] + 1) - 1, {n, 1, 40}]
%o A286264 (PARI) Vec(x*(3 - x + x^2 + x^3) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ _Colin Barker_, May 05 2017
%o A286264 (Magma) [3/2 - (-1)^n/2 + n^2 : n in [1..100]]; // _Wesley Ivan Hurt_, May 05 2017
%Y A286264 Cf. A007918 (nextprime), A151800 (version 2).
%K A286264 nonn,easy
%O A286264 1,1
%A A286264 _Ralf Steiner_, May 05 2017
%E A286264 More terms from _Colin Barker_, May 05 2017