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 A277977 #16 Aug 28 2018 00:07:50 %S A277977 0,1,19,96,298,715,1461,2674,4516,7173,10855,15796,22254,30511,40873, %T A277977 53670,69256,88009,110331,136648,167410,203091,244189,291226,344748, %U A277977 405325,473551,550044,635446,730423,835665,951886,1079824,1220241,1373923,1541680,1724346 %N A277977 a(n) = n*(1-3n+2*n^2+2*n^3)/2. %C A277977 For n>=3, a(n) is the second Zagreb index of the graph obtained by joining one vertex of a complete graph K[n] with each vertex of a second complete graph K[n]. %C A277977 The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g. %H A277977 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A277977 G.f.: x*(1+x)*(1+13*x-2*x^2)/(1-x)^5. - _Robert Israel_, Nov 07 2016 %e A277977 a(4) = 298. Indeed, the corresponding graph has 16 edges. We list the degrees of their endpoints: (3,3), (3,3), (3,3), (3,7), (3,7), (3,7), (4,4), (4,4), (4,4), (4,4), (4,4), (4,4), (4,7), (4,7), (4,7), (4,7). Then, the second Zagreb index is 3*9 + 3*21 + 6*16 + 4*28 = 298. %p A277977 seq((1/2)*n*(1-3*n+2*n^2+2*n^3), n = 0 .. 45); %o A277977 (PARI) a(n) = n*(1-3*n+2*n^2+2*n^3)/2 \\ _Felix Fröhlich_, Nov 07 2016 %o A277977 (PARI) concat(0, Vec(x*(1+x)*(1+13*x-2*x^2)/(1-x)^5 + O(x^40))) \\ _Felix Fröhlich_, Nov 07 2016 %Y A277977 Cf. A213820. %K A277977 nonn,easy %O A277977 0,3 %A A277977 _Emeric Deutsch_, Nov 07 2016