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Number of (4+1) X (n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.
Row 4 of A264476.
Empirical: a(n) = 9*a(n-2) + 54*a(n-3) + 60*a(n-4) - 54*a(n-5) - 279*a(n-6) - 270*a(n-7) + 64*a(n-8) - 864*a(n-9) - 1728*a(n-10) for n>11.
Empirical g.f.: x*(1 + 8*x + 7*x^2 - 6*x^3 - 180*x^4 - 98*x^5 + 211*x^6 + 294*x^7 - 208*x^8 + 576*x^9 + 2496*x^10) / (1 - 9*x^2 - 54*x^3 - 60*x^4 + 54*x^5 + 279*x^6 + 270*x^7 - 64*x^8 + 864*x^9 + 1728*x^10). - Colin Barker, Jan 08 2019
Some solutions for n=4:
Cf. Row 4 of A264476.
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R. H. Hardin, <a href="/A264478/b264478.txt">Table of n, a(n) for n = 1..210</a>
allocated for R. H. Hardin
Number of (4+1)X(n+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.
1, 8, 16, 120, 456, 2272, 11044, 49200, 236196, 1113296, 5157772, 24352896, 114256032, 534574312, 2511482164, 11778946872, 55224573264, 259130295272, 1215413555584, 5700599522328, 26741489475588, 125432405841016
1,2
Row 4 of A264476.
Empirical: a(n) = 9*a(n-2) +54*a(n-3) +60*a(n-4) -54*a(n-5) -279*a(n-6) -270*a(n-7) +64*a(n-8) -864*a(n-9) -1728*a(n-10) for n>11
Some solutions for n=4
..6..7..8..9..3....6..7..1..9..3....6..7..1..2..3....6..7..1..2..3
..0.12..2.14..4....0.12..2.14..4....0.12.13.14..4....0..5.13.14..4
..5.10..1.19.13....5.17.18.19.13....5.10.11.19..9...16.17.18.19..9
.21.11.16.24.18...10.11.16.24..8...21.22.16.24..8...10.11.12.24..8
.15.20.17.22.23...15.20.21.22.23...15.20.17.18.23...15.20.21.22.23
Cf. A264476.
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nonn
R. H. Hardin, Nov 14 2015
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