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 A326657 #30 Sep 26 2019 03:39:35 %S A326657 1,0,5,6,13,16,25,30,41,48,61,70,85,96,113,126,145,160,181,198,221, %T A326657 240,265,286,313,336,365,390,421,448,481,510,545,576,613,646,685,720, %U A326657 761,798,841,880,925,966,1013,1056,1105,1150,1201,1248,1301,1350,1405,1456,1513,1566,1625,1680 %N A326657 a(n) = 4*floor(n/2) + ceiling((n-1)^2/2). %C A326657 a(n) gives the maximum number of inversions in a permutation on n + 2 symbols consisting of a single n-cycle and 2 fixed points. %C A326657 Sequence is a diagonal of A326296. %H A326657 Colin Barker, <a href="/A326657/b326657.txt">Table of n, a(n) for n = 0..1000</a> %H A326657 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1). %F A326657 a(n) = 4*floor(n/2) + ceiling((n-1)^2/2). %F A326657 a(n) = A326296(2 + n, n) for n > 0. %F A326657 From _Colin Barker_, Sep 15 2019: (Start) %F A326657 G.f.: (1 - 2*x + 5*x^2 - 2*x^3) / ((1 - x)^3*(1 + x)). %F A326657 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n >= 4. %F A326657 a(n) = (-1 + 5*(-1)^n + 4*n + 2*n^2) / 4. %F A326657 (End) %F A326657 E.g.f.: (1/4)*(5*exp(-x) + exp(x)*(-1 + 6*x + 2*x^2)). - _Stefano Spezia_, Sep 16 2019 after _Colin Barker_ %o A326657 (PARI) a(n) = 4*floor(n/2) + ceil((n-1)^2/2) \\ _Andrew Howroyd_, Sep 23 2019 %o A326657 (PARI) Vec((1 - 2*x + 5*x^2 - 2*x^3) / ((1 - x)^3*(1 + x)) + O(x^40)) \\ _Andrew Howroyd_, Sep 23 2019 %Y A326657 Diagonal of A326296. %K A326657 nonn,easy %O A326657 0,3 %A A326657 _M. Ryan Julian Jr._, Sep 12 2019