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 A189145 #26 Oct 15 2021 20:00:24
%S A189145 1,1,4,16,36,81,225,625,1600,4096,10816,28561,74529,194481,509796,
%T A189145 1336336,3496900,9150625,23961025,62742241,164249856,429981696,
%U A189145 1125736704,2947295521,7716041281,20200652641,52886200900,138458410000
%N A189145 Number of n X 2 array permutations with each element making zero or one knight moves.
%C A189145 Column 2 of A189150.
%C A189145 a(n+2) is number of ways to place k non-attacking knights on a 2 x n board, sum over all k>=0.
%H A189145 R. H. Hardin, <a href="/A189145/b189145.txt">Table of n, a(n) for n = 1..200</a>
%F A189145 Empirical: a(n) = 3*a(n-1) -3*a(n-2) +6*a(n-3) -6*a(n-5) +3*a(n-6) -3*a(n-7) +a(n-8).
%F A189145 Empirical: G.f. -x*(1-2*x+4*x^2+x^3+3*x^5+x^7-6*x^4-3*x^6) / ( (x-1)*(1+x)*(x^2-3*x+1)*(x^4+3*x^2+1) ). - _R. J. Mathar_, Oct 15 2011
%F A189145 Explicit formula: ((3+sqrt(5))/2)^(n+2)/25 + ((3-sqrt(5))/2)^(n+2)/25 + (((sqrt(5)+1)/2)^(n+2) + ((sqrt(5)-1)/2)^(n+2))*4*cos((Pi*n)/2)/25 + (((sqrt(5)+1)/2)^(n+2) - ((sqrt(5)-1)/2)^(n+2))*2*sin((Pi*n)/2)/25 + 1/10 + 7/50*(-1)^n. - _Vaclav Kotesovec_, Nov 07 2011
%e A189145 All solutions for 3X2
%e A189145 ..0..1....0..4....5..1....5..4
%e A189145 ..2..3....2..3....2..3....2..3
%e A189145 ..4..5....1..5....4..0....1..0
%t A189145 Table[FullSimplify[LucasL[2n+4]/25 + (3*Fibonacci[n+1] + Fibonacci[n]) * (2*Cos[(Pi*n)/2] + Sin[(Pi*n)/2])*2/25 + 7*(-1)^n/50 + 1/10], {n,1,20}] (* _Vaclav Kotesovec_, Nov 07 2011 *)
%K A189145 nonn
%O A189145 1,3
%A A189145 _R. H. Hardin_, Apr 17 2011