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Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.
1

%I #6 Nov 10 2015 12:12:55

%S 15,160,2076,25968,331130,4213002,53712998,684799391,8732881192,

%T 111369466097,1420333983945,18114184500130,231020023102857,

%U 2946329450622616,37576249111921443,479231893077739510

%N Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 filled by rows with each element moved a city block distance of 0 or 1, and rows and columns in increasing lexicographic order.

%C Column 3 of A263519.

%H R. H. Hardin, <a href="/A263514/b263514.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 21*a(n-1) -79*a(n-2) -673*a(n-3) +4265*a(n-4) +6333*a(n-5) -74971*a(n-6) +5561*a(n-7) +663755*a(n-8) -476684*a(n-9) -3383618*a(n-10) +3581474*a(n-11) +10537915*a(n-12) -13432805*a(n-13) -20667455*a(n-14) +29866250*a(n-15) +25992764*a(n-16) -42071720*a(n-17) -21067986*a(n-18) +38850164*a(n-19) +10841024*a(n-20) -23910247*a(n-21) -3353599*a(n-22) +9844537*a(n-23) +516051*a(n-24) -2689555*a(n-25) +5229*a(n-26) +476619*a(n-27) -15719*a(n-28) -52417*a(n-29) +2440*a(n-30) +3298*a(n-31) -150*a(n-32) -101*a(n-33) +3*a(n-34) +a(n-35)

%e Some solutions for n=4

%e ..0..1..2..3....0..1..3..7....0..1..6..7....0..1..2..3....0..1..2..3

%e ..4..6..5..7....4..5..2.11....4..5..2..3....4..9..6..7....5..4..7.11

%e ..8..9.14.10....9..8..6.10....8..9.11.10....8..5.10.15....9..8..6.10

%e .12.13.15.11...16.12.13.15...12.14.13.19...16.12.18.11...12.13.14.15

%e .17.16.19.18...17.18.14.19...17.16.18.15...17.13.14.19...17.16.18.19

%Y Cf. A263519.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 19 2015