This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A248800 #44 Jan 30 2022 19:28:24
%S A248800 2,2,6,10,18,26,38,50,66,82,102,122,146,170,198,226,258,290,326,362,
%T A248800 402,442,486,530,578,626,678,730,786,842,902,962,1026,1090,1158,1226,
%U A248800 1298,1370,1446,1522,1602,1682,1766,1850,1938,2026,2118
%N A248800 a(n) = (2*n^2 + 3 + (-1)^n)/2.
%C A248800 Numbers belonging to A016825: a(n) = A016825( A002620(n) ). - _Bruno Berselli_, Oct 15 2014
%C A248800 For n>1, a(n) is the number of row vectors of length 2n with entries in [1,n], first entry 1, with maximum inner distance. That is, vectors where the modular distance between adjacent entries is at least (n-2)/2. Modular distance is the minimum of remainders of (x - y) and (y - x) when dividing by n. Geometrically, this metric counts how far the integers mod n are from each other if 1 and n are adjacent as on a circle. - _Omar Aceval Garcia_, Jan 30 2021
%H A248800 G. C. Greubel, <a href="/A248800/b248800.txt">Table of n, a(n) for n = 0..1000</a>
%H A248800 Omar Aceval Garcia, <a href="https://arxiv.org/abs/2112.13912">On the Number of Maximum Inner Distance Latin Squares</a>, arXiv:2112.13912 [math.CO], 2021.
%H A248800 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A248800 a(n) = A000290(n) + A000034(n+1) = 4*A002620(n) + 2.
%F A248800 a(n+1) = 2*A080827(n+1) = (n+2)^2 - A042964(n+1) = a(n) + 2*n + 1 -(-1)^n.
%F A248800 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). - _Colin Barker_, Oct 15 2014
%F A248800 G.f.: 2*(1-x+x^2+x^3) / ((1-x)^3*(x+1)). - _Colin Barker_, Oct 15 2014
%F A248800 E.g.f.: cosh(x) + (1 + x + x^2)*exp(x). - _G. C. Greubel_, Dec 14 2021
%F A248800 a(2n) = A005899(n) for n > 0, a(2n+1) = A069894(n). - _Omar Aceval Garcia_, Dec 30 2021
%t A248800 Table[n^2 + 3/2 + (-1)^n/2, {n, 0, 50}] (* _Bruno Berselli_, Oct 15 2014 *)
%t A248800 CoefficientList[Series[2(x^3+x^2-x+1)/((1-x)^3 (x+1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2014 *)
%t A248800 LinearRecurrence[{2,0,-2,1},{2,2,6,10},60] (* _Harvey P. Dale_, Apr 08 2019 *)
%o A248800 (PARI) Vec(-2*(x^3+x^2-x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Oct 15 2014
%o A248800 (Magma) [n^2+3/2+(-1)^n/2: n in [0..50]]; // _Vincenzo Librandi_, Oct 15 2014
%o A248800 (Sage) [(2*n^2 +3 +(-1)^n)/2 for n in (0..50)] # _G. C. Greubel_, Dec 14 2021
%Y A248800 Cf. A000034, A000290, A002620, A016825, A042964, A080827, A168273, A005899, A069894.
%K A248800 nonn,easy
%O A248800 0,1
%A A248800 _Paul Curtz_, Oct 14 2014
%E A248800 Typo in data fixed by _Colin Barker_, Oct 15 2014