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%I #6 Nov 10 2015 12:15:51
%S 23,208,2076,18369,158109,1317780,10791350,87194833,698250904,
%T 5555688785,44005119429,347432212188,2736799922735,21523189213085,
%U 169068961542156,1326964403390558,10408686351322363,81610767953922967,639685545725575292
%N Number of (3+1)X(n+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 Row 3 of A263519.
%H R. H. Hardin, <a href="/A263521/b263521.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 18*a(n-1) -83*a(n-2) -203*a(n-3) +2162*a(n-4) -633*a(n-5) -21640*a(n-6) +20040*a(n-7) +120424*a(n-8) -126960*a(n-9) -418440*a(n-10) +397224*a(n-11) +935858*a(n-12) -706132*a(n-13) -1333426*a(n-14) +768238*a(n-15) +1198092*a(n-16) -535990*a(n-17) -670920*a(n-18) +245400*a(n-19) +229128*a(n-20) -73408*a(n-21) -45880*a(n-22) +13832*a(n-23) +4959*a(n-24) -1502*a(n-25) -235*a(n-26) +77*a(n-27) +2*a(n-28) -a(n-29)
%e Some solutions for n=4
%e ..0..1..2..3..4....0..1..2..3..4....0..1..2..8..9....0..2..3..8..9
%e .10..5.12..8.14....6..5..7.13..9....5..6..7..3..4....5..1..6..7..4
%e .15..6..7.18..9...15.10.12..8.14...10.11.12.13.14...11.10.17.12.13
%e .16.11.17.13.19...16.11.17.19.18...15.16.17.19.18...15.16.18.19.14
%Y Cf. A263519.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 19 2015
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