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A189451 Number of 3Xn array permutations with each element moving zero or one space horizontally or diagonally.

%I A189451 #7 Jul 22 2025 11:45:43
%S A189451 1,13,80,666,5080,40106,313136,2455013,19221095,150562121,1179185280,
%T A189451 9235771513,72336253737,566554489205,4437377818704,34754532606346,
%U A189451 272205182385544,2131971340412858,16698071766102576,130782997877002493
%N A189451 Number of 3Xn array permutations with each element moving zero or one space horizontally or diagonally.
%C A189451 Row 3 of A189449
%H A189451 R. H. Hardin, <a href="/A189451/b189451.txt">Table of n, a(n) for n = 1..200</a>
%F A189451 Empirical: a(n) = 6*a(n-1) +26*a(n-2) -72*a(n-3) -195*a(n-4) +284*a(n-5) +555*a(n-6) -424*a(n-7) -555*a(n-8) +284*a(n-9) +195*a(n-10) -72*a(n-11) -26*a(n-12) +6*a(n-13) +a(n-14)
%e A189451 Some solutions for 3X3
%e A189451 ..1..0..2....0..2..1....0..1..2....0..2..1....0..1..2....1..0..2....0..5..2
%e A189451 ..3..4..5....3..8..5....4..3..5....4..3..5....4..3..5....7..5..4....3..4..1
%e A189451 ..7..6..8....6..7..4....6..8..7....6..8..7....7..6..8....6..3..8....6..8..7
%K A189451 nonn
%O A189451 1,2
%A A189451 _R. H. Hardin_ Apr 22 2011