A263503 - OEIS

%I #9 May 28 2021 13:41:49

%S 8,59,360,2196,13704,85189,528559,3280284,20360536,126365281,

%T 784254518,4867282254,30207532735,187474861266,1163511187403,

%U 7221010676326,44815200779002,278133097211273,1726155767731454,10712905866198251

%N Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 0 1 or 2, and rows and columns in increasing lexicographic order.

%C Column 1 of A263506.

%H R. H. Hardin, <a href="/A263503/b263503.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) -2*a(n-2) -12*a(n-3) -18*a(n-4) -138*a(n-5) +58*a(n-6) +109*a(n-7) +35*a(n-8) +97*a(n-9) -36*a(n-10) -60*a(n-11) +4*a(n-12) -2*a(n-13) +a(n-15).

%e Some solutions for n=4

%e ..0..1....0..5....0..5....0..1....0..1....1..2....0..1....0..5....1..3....0..3

%e ..2..4....2..1....1..3....2..7....2..3....5..0....2..5....1..4....2..0....1..2

%e ..5..3....3..7....2..4....3..5....4..6....7..3....3..7....2..3....6..5....4..7

%e ..6..8....4..6....8..6....4..9....7..5....8..4....6..4....6..9....7..4....5..8

%e ..7..9....9..8....9..7....8..6....8..9....9..6....9..8....8..7....9..8....9..6

%Y Cf. A263506.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 19 2015