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A264343 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 0,1 or 1,2.

%I A264343 #6 Sep 07 2022 22:27:30
%S A264343 16,233,4900,70669,1243225,20386617,345358201,5804687049,97945201592,
%T A264343 1651466105125,27856916781264,469861192549345,7925440297808628,
%U A264343 133682668669239757,2254906043186042569,38034843997925237049
%N A264343 Number of (3+1) X (n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 0,1 or 1,2.
%C A264343 Row 3 of A264341.
%H A264343 R. H. Hardin, <a href="/A264343/b264343.txt">Table of n, a(n) for n = 1..210</a>
%F A264343 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 A264343 Some solutions for n=4
%e A264343 ..0..2..1..3..4....7..8..3..2..4....1..0..9..3..4....0..8..1..4..3
%e A264343 .12..6..8..7..9....5..6..0..1..9....5..7..6..8..2....5..6.14..9..2
%e A264343 .10.11..5.13.14...17.10.13.12.14...11.12.19.13.14...17.11.13.12..7
%e A264343 .15.17.16.18.19...16.15.18.11.19...15.16.10.17.18...15.16.10.18.19
%Y A264343 Cf. A264341.
%K A264343 nonn
%O A264343 1,1
%A A264343 _R. H. Hardin_, Nov 11 2015