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A264275 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

%I A264275 #11 May 27 2025 16:40:12
%S A264275 64,1800,50625,1143000,25806400,600090240,13954224384,323177889984,
%T A264275 7484754845584,173362944655124,4015456912022689,93006360976711231,
%U A264275 2154221392895732449,49896286681978765567,1155702674228671452961,26768498558076022772640,620014585959103244313600
%N A264275 Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 1,0 or 1,2.
%H A264275 R. H. Hardin, <a href="/A264275/b264275.txt">Table of n, a(n) for n = 1..210</a>
%F A264275 Empirical: a(n) = 24*a(n-1) -467*a(n-3) +625*a(n-4) -5260*a(n-5) -15671*a(n-6) +466107*a(n-7) -420812*a(n-8) +879839*a(n-9) -157761*a(n-10) -732744*a(n-11) +1973397*a(n-12) -2238123*a(n-13) +1652184*a(n-14) -1326213*a(n-15) -1823409*a(n-16) +641268*a(n-17) -3529953*a(n-18) -222939*a(n-19) -250668*a(n-20) -21735*a(n-21) +9153*a(n-22) +2916*a(n-24) +243*a(n-25) for n>27.
%e A264275 Some solutions for n=3:
%e A264275 ..4..7..2..3....0..5..2..3....0..5..2..3....4..1..2..3....4..7..2..3
%e A264275 ..0..1.10.11....4..1.10.11....8.11..6..1....0..9.10..7....0..5.10..1
%e A264275 ..8..5..6.15....8.13..6..7....4.13.14..7...14.15..6..5....8.13..6.11
%e A264275 .12.17.14..9...12..9.14.15...12..9.10.19...12.17..8.11...16..9.14.19
%e A264275 .16.13.18.19...16.17.18.19...16.17.18.15...16.13.18.19...12.17.18.15
%Y A264275 Row 4 of A264272.
%K A264275 nonn
%O A264275 1,1
%A A264275 _R. H. Hardin_, Nov 10 2015