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 A005390 M5264 #23 Nov 18 2022 03:42:12
%S A005390 1,37,1072,32675,1024028,32463802,1033917350,32989068162,
%T A005390 1053349394128,33643541208290,1074685815276400,34330607094625734,
%U A005390 1096704136430950646,35034883701169366742,1119214052513009716324,35754123580486507079548
%N A005390 Number of Hamiltonian circuits on 2n X 6 rectangle.
%D A005390 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005390 G. C. Greubel, <a href="/A005390/b005390.txt">Table of n, a(n) for n = 1..660</a>
%H A005390 Andre Poenitz, <a href="http://mathematik.htwm.de/software/gedit/index.html.en">Some software</a>
%H A005390 T. G. Schmalz, G. E. Hite and D. J. Klein, <a href="http://dx.doi.org/10.1088/0305-4470/17/2/029">Compact self-avoiding circuits on two-dimensional lattices</a>, J. Phys. A 17 (1984), 445-453.
%H A005390 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (53,-802,4463,-10928,13708,-12157,7032,-11272, 15064,-13336,5948,-792,-96,-4).
%F A005390 a(n) = A145401(2*n). - _Sean A. Irvine_, Jun 11 2016
%F A005390 G.f.: x*(1 - 16*x - 87*x^2 + 1070*x^3 - 2206*x^4 + 1960*x^5 - 2448*x^6 + 1053*x^7 + 392*x^8 - 1517*x^9 + 1012*x^10 - 120*x^11 - 28*x^12 - 2*x^13)/(1 - 53*x + 802*x^2 - 4463*x^3 + 10928*x^4 - 13708*x^5 + 12157*x^6 - 7032*x^7 + 11272*x^8 - 15064*x^9 + 13336*x^10 - 5948*x^11 + 792*x^12 + 96*x^13 + 4*x^14). - _G. C. Greubel_, Nov 18 2022
%t A005390 Rest@CoefficientList[Series[x*(1 -16*x -87*x^2 +1070*x^3 -2206*x^4 +1960*x^5 -2448*x^6 +1053*x^7 +392*x^8 -1517*x^9 +1012*x^10 -120*x^11 -28*x^12 -2*x^13)/(1 -53*x + 802*x^2 -4463*x^3 +10928*x^4 -13708*x^5 +12157*x^6 -7032*x^7 +11272*x^8 -15064*x^9 +13336*x^10 -5948*x^11 +792*x^12 +96*x^13 +4*x^14), {x,0,40}], x] (* _G. C. Greubel_, Nov 17 2022 *)
%o A005390 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1 -16*x -87*x^2 +1070*x^3 -2206*x^4 +1960*x^5 -2448*x^6 +1053*x^7 +392*x^8 -1517*x^9 +1012*x^10 -120*x^11 -28*x^12 -2*x^13)/(1 -53*x + 802*x^2 -4463*x^3 +10928*x^4 -13708*x^5 +12157*x^6 -7032*x^7 +11272*x^8 -15064*x^9 +13336*x^10 -5948*x^11 +792*x^12 +96*x^13 +4*x^14) )); // _G. C. Greubel_, Nov 17 2022
%o A005390 (SageMath)
%o A005390 def g(x): return x*(1 -16*x -87*x^2 +1070*x^3 -2206*x^4 +1960*x^5 -2448*x^6 +1053*x^7 +392*x^8 -1517*x^9 +1012*x^10 -120*x^11 -28*x^12 -2*x^13)/(1 -53*x + 802*x^2 -4463*x^3 +10928*x^4 -13708*x^5 +12157*x^6 -7032*x^7 +11272*x^8 -15064*x^9 +13336*x^10 -5948*x^11 +792*x^12 +96*x^13 +4*x^14)
%o A005390 def A005390_list(prec):
%o A005390 P.<x> = PowerSeriesRing(ZZ, prec)
%o A005390 return P( g(x) ).list()
%o A005390 a=A005390_list(40); a[1:] # _G. C. Greubel_, Nov 17 2022
%Y A005390 Cf. A145401.
%K A005390 nonn
%O A005390 1,2
%A A005390 _N. J. A. Sloane_
%E A005390 More terms from André Pönitz (poenitz(AT)htwm.de), Jun 11 2003