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A263587 Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 1 or 2, and rows and columns in increasing lexicographic order. 1

%I

%S 1,6,12,31,89,230,536,1171,2439,4882,9470,17935,33331,60994,110208,

%T 197059,349285,614522,1074316,1867855,3232059,5569206,9560842,

%U 16359331,27909479,47487870,80606196,136522471,230766449,389355662,655827200

%N Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 1 or 2, and rows and columns in increasing lexicographic order.

%H R. H. Hardin, <a href="/A263587/b263587.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) - 2*a(n-5) + 3*a(n-6) - a(n-8) for n>9.

%F Empirical g.f.: x*(1 + 2*x - 7*x^2 + 11*x^3 + 13*x^4 + 7*x^5 + 8*x^6 + 5*x^7 + 2*x^8) / ((1 - x)^2*(1 + x^2)*(1 - x - x^2)^2). - _Colin Barker_, Jan 02 2019

%e Some solutions for n=4:

%e ..1..3..6..8..9....1..5..7..8..9....2..5..6..8..9....1..2..3..8..9

%e ..7..0..5..2..4....6..0..2..3..4....7..0..1..3..4....6..0..5..4..7

%Y Row 1 of A263586.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 22 2015

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Last modified February 8 23:03 EST 2023. Contains 360153 sequences. (Running on oeis4.)