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A189431 Number of nX5 array permutations with each element not moving, or moving one space N, SW or SE.

%I A189431 #7 Jul 22 2025 11:44:33
%S A189431 1,8,65,571,5680,52241,493941,4681376,44341381,420325171,3983969024,
%T A189431 37773176577,358128315977,3395458162288,32193312416793,
%U A189431 305234770125411,2894031473957664,27439272582314225,260161002358646165
%N A189431 Number of nX5 array permutations with each element not moving, or moving one space N, SW or SE.
%C A189431 Column 5 of A189435
%H A189431 R. H. Hardin, <a href="/A189431/b189431.txt">Table of n, a(n) for n = 1..200</a>
%F A189431 Empirical: a(n) = 9*a(n-1) -a(n-2) +88*a(n-3) -133*a(n-4) -1241*a(n-5) -6173*a(n-6) +1260*a(n-7) -35412*a(n-8) +81872*a(n-9) +143920*a(n-10) -260064*a(n-11) +2649517*a(n-12) -4380197*a(n-13) -10792671*a(n-14) +17380340*a(n-15) +17309201*a(n-16) +82171225*a(n-17) -34858151*a(n-18) -315791376*a(n-19) +66797872*a(n-20) -231978696*a(n-21) +734413152*a(n-22) +760013432*a(n-23) -1058202998*a(n-24) -2085612850*a(n-25) -7191772318*a(n-26) +7045350632*a(n-27) +3638845930*a(n-28) +3481732186*a(n-29) +8643493314*a(n-30) -7150172088*a(n-31) +12002114312*a(n-32) -17160930824*a(n-33) -1460727184*a(n-34) +58198351544*a(n-35) -1772883650*a(n-36) -13721600534*a(n-37) +7148283886*a(n-38) -31542922592*a(n-39) -28065877170*a(n-40) -27375326650*a(n-41) -29235699066*a(n-42) -15582339728*a(n-43) -48617808*a(n-44) +4434566056*a(n-45) -693712320*a(n-46) +2141282408*a(n-47) +2851911223*a(n-48) +1535350953*a(n-49) -85925633*a(n-50) -94378304*a(n-51) +529827963*a(n-52) -125838145*a(n-53) -233700005*a(n-54) -61208340*a(n-55) +22857068*a(n-56) +42821976*a(n-57) +4528704*a(n-58) -1484088*a(n-59) +1003221*a(n-60) -1054917*a(n-61) -305775*a(n-62) -6804*a(n-63) -63423*a(n-64) +6561*a(n-65) +6561*a(n-66)
%e A189431 Some solutions for 3X5
%e A189431 ..5..1..2..8..9....0..1..2..3..4....0..1..2..3..4....0..1..2..8..4
%e A189431 .10..0..7..4..3....5..6.12.13..9....5.11.12.13.14...10.11..3.13..9
%e A189431 ..6.11.12.13.14...10.11..8..7.14...10..7..6..9..8....6..5.12..7.14
%K A189431 nonn
%O A189431 1,2
%A A189431 _R. H. Hardin_ Apr 22 2011