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A189452 Number of 4Xn array permutations with each element moving zero or one space horizontally or diagonally.

%I A189452 #7 Jul 22 2025 11:45:50
%S A189452 1,34,400,7300,118128,2008890,33735505,569476049,9601403672,
%T A189452 161963813841,2731821630753,46079554836082,777248318344360,
%U A189452 13110321921956724,221139603633268744,3730094981047721690,62917755232156271921
%N A189452 Number of 4Xn array permutations with each element moving zero or one space horizontally or diagonally.
%C A189452 Row 4 of A189449
%H A189452 R. H. Hardin, <a href="/A189452/b189452.txt">Table of n, a(n) for n = 1..200</a>
%F A189452 Empirical: a(n) = 14*a(n-1) +139*a(n-2) -1260*a(n-3) -7702*a(n-4) +43762*a(n-5) +217890*a(n-6) -744490*a(n-7) -3383575*a(n-8) +6630690*a(n-9) +29495043*a(n-10) -31906396*a(n-11) -148462702*a(n-12) +80910366*a(n-13) +438178264*a(n-14) -91294992*a(n-15) -756685497*a(n-16) +756685497*a(n-18) +91294992*a(n-19) -438178264*a(n-20) -80910366*a(n-21) +148462702*a(n-22) +31906396*a(n-23) -29495043*a(n-24) -6630690*a(n-25) +3383575*a(n-26) +744490*a(n-27) -217890*a(n-28) -43762*a(n-29) +7702*a(n-30) +1260*a(n-31) -139*a(n-32) -14*a(n-33) +a(n-34)
%e A189452 Some solutions for 4X3
%e A189452 ..0..1..2....1..0..2....0..2..1....1..0..2....0..2..1....4..0..2....0..5..2
%e A189452 ..4..3..5....3..8..5....4..3..5....4..3..5....7..8..5....3..5..1....7..8..1
%e A189452 ..6.11..8....6..7..4....6..7..8....6..7..8...10..3..4...10..7..8....6..3..4
%e A189452 ..9.10..7....9.11.10....9.10.11....9.11.10....9..6.11....9..6.11....9.10.11
%K A189452 nonn
%O A189452 1,2
%A A189452 _R. H. Hardin_ Apr 22 2011