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 A298125 #23 Feb 05 2018 09:36:50 %S A298125 1,3,7,19,37,61,91,127,169,217,271,331,397,469,547,631,721,817,919, %T A298125 1027,1141,1261,1387,1519,1657,1801,1951,2107,2269,2437,2611,2791, %U A298125 2977,3169,3367,3571,3781,3997,4219,4447,4681,4921,5167,5419,5677,5941,6211,6487 %N A298125 The hex numbers (A003215) together with 3. %C A298125 Apart from the term 3, these are precisely the sizes of hexagonal clusters of circles in the A_2 (or hexagonal) lattice. %C A298125 These numbers include many common numbers of strands used in cables. %H A298125 Colin Barker, <a href="/A298125/b298125.txt">Table of n, a(n) for n = 1..1000</a> %H A298125 B. K. Teo and N. J. A. Sloane, <a href="http://dx.doi.org/10.1021/ic00220a025">Magic numbers in polygonal and polyhedral clusters</a>, Inorgan. Chem. 24 (1985), 4545-4558. %H A298125 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wire#Number_of_strands">Wire: Number of strands</a> %H A298125 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A298125 From _Colin Barker_, Feb 05 2018: (Start) %F A298125 G.f.: x*(1 + x^2 + 6*x^3 - 2*x^4) / (1 - x)^3. %F A298125 a(n) = 7 - 9*n + 3*n^2 for n>2. %F A298125 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5. %F A298125 (End) %o A298125 (PARI) Vec(x*(1 + x^2 + 6*x^3 - 2*x^4) / (1 - x)^3 + O(x^60)) \\ _Colin Barker_, Feb 05 2018 %Y A298125 Cf. A003215. %K A298125 nonn,easy %O A298125 1,2 %A A298125 _Brian Watson_, Jan 13 2018 %E A298125 Entry revised by _N. J. A. Sloane_, Jan 22 2018