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 A163003 #10 Jan 13 2023 14:42:15 %S A163003 1,8,45,234,1193,6049,30616,154861,783150,3960215,20025500,101261654, %T A163003 512042141,2589202874,13092613725,66204360820,334770228305, %U A163003 1692805481383,8559872259604,43284012160451,218870755473698,1106746006355201,5596392811360844,28298825854292256 %N A163003 Number of n X 3 binary arrays with all 1s connected and a path of 1s from upper left corner to lower right corner. %H A163003 R. H. Hardin, <a href="/A163003/b163003.txt">Table of n, a(n) for n=1..100</a> %F A163003 From _R. J. Mathar_, Aug 11 2009: (Start) %F A163003 Empirical: a(n) = 8*a(n-1) -17*a(n-2) +10*a(n-3) +6*a(n-4) -14*a(n-5) +7*a(n-6) +6*a(n-7) -a(n-8). %F A163003 Empirical g.f.: -x*(1+x)*(x^4-x^3+x^2+x-1)/ ((x^2+x-1)*(x^6-7*x^5+x^4+6*x^3-11*x^2+7*x-1)). (End) %F A163003 The above empirical formulas are correct. - _Andrew Howroyd_, Jan 06 2023 %Y A163003 Row 3 of A359573. %K A163003 nonn %O A163003 1,2 %A A163003 _R. H. Hardin_, Jul 20 2009