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 A277983 #32 Feb 16 2025 08:33:37
%S A277983 36,12,96,288,588,996,1512,2136,2868,3708,4656,5712,6876,8148,9528,
%T A277983 11016,12612,14316,16128,18048,20076,22212,24456,26808,29268,31836,
%U A277983 34512,37296,40188,43188,46296,49512,52836,56268,59808,63456,67212,71076,75048,79128,83316
%N A277983 a(n) = 54*n^2 - 78*n + 36.
%C A277983 For n>=1, a(n) is the second Zagreb index of the triangular grid graph T[n] (see the West reference, p. 390). The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
%C A277983 The M-polynomial of the triangular grid graph T[n] is M(T[n], x, y) = 6*x^2*y^4 + 3*(n-1)*x^4*y^4 +6*(n-2)*x^4*y^6+3*(n-2)*(n-3)*x^6*y^6/2.
%D A277983 D. B. West, Introduction to Graph Theory, 2nd edition, Prentice-Hall, 2001.
%H A277983 E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A277983 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph">.html">Triangular Grid Graph</a>
%H A277983 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A277983 O.g.f.: 12*(14*x^2 - 8*x + 3)/(1 - x)^3.
%F A277983 E.g.f.: 6*(9*x^2 - 4*x + 6)*exp(x). - _Bruno Berselli_, Nov 11 2016
%F A277983 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Wesley Ivan Hurt_, Jan 15 2022
%F A277983 a(n) = 12*A064225(n-1). - _R. J. Mathar_, Jul 22 2022
%p A277983 seq(54*n^2-78*n+36, n=0..40);
%t A277983 Table[54 n^2 - 78 n + 36, {n, 0, 50}] (* _Bruno Berselli_, Nov 11 2016 *)
%o A277983 (Sage) [54*n^2-78*n+36 for n in range(50)] # _Bruno Berselli_, Nov 11 2016
%o A277983 (Magma) [54*n^2-78*n+36: n in [0..50]]; // _Bruno Berselli_, Nov 11 2016
%o A277983 (PARI) a(n)=54*n^2-78*n+36 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A277983 Cf. A153792.
%K A277983 nonn,easy
%O A277983 0,1
%A A277983 _Emeric Deutsch_, Nov 11 2016