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 A344679 #46 Nov 09 2021 06:05:38 %S A344679 0,0,86,544,1854,4688,9910,18576,31934,51424,78678,115520,163966, %T A344679 226224,304694,401968,520830,664256,835414,1037664,1274558,1549840, %U A344679 1867446,2231504,2646334,3116448,3646550,4241536,4906494,5646704,6467638,7374960,8374526,9472384,10674774 %N A344679 Number of 2-matchings of the n-th centered square grid graph. %C A344679 Number of ways two dominoes can be placed on an "other" Aztec Diamonds chessboard. %H A344679 Nicolas Bělohoubek, <a href="/A344679/a344679.pdf">Visualization of 3rd term</a>. %H A344679 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Figurate/figurate2.html">1.2.5 The "other" Aztec Diamonds</a> %H A344679 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A344679 a(n) = 2*(n-2)*(4n^3-8n^2+n+4) for n > 1. %F A344679 From _Stefano Spezia_, Aug 17 2021: (Start) %F A344679 G.f.: 2*x^3*(43 + 57*x - 3*x^2 - x^3)/(1 - x)^5. %F A344679 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 6. (End) %e A344679 For n=1 there is no way to place 2 dominoes in the centered square grid graphs, because they don't have enough space to be placed, so a(1)=0. %e A344679 For n=2 there is no way to place 2 dominoes in the centered square grid graphs, because the first domino will cover the center square every time, so a(2)=0. %Y A344679 Cf. A001844, A242856. %K A344679 nonn,easy %O A344679 1,3 %A A344679 _Nicolas Bělohoubek_, Aug 17 2021