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A201539 T(n,k)=Number of nXk 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.

%I A201539 #7 Jul 22 2025 16:17:49
%S A201539 0,3,3,3,9,3,6,25,25,6,9,69,111,69,9,13,175,633,633,175,13,18,410,
%T A201539 3354,7799,3354,410,18,24,899,16393,91425,91425,16393,899,24,31,1859,
%U A201539 72811,983981,2446147,983981,72811,1859,31,39,3649,293831,9526987,61807736
%N A201539 T(n,k)=Number of nXk 0..2 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
%C A201539 Table starts
%C A201539 ..0....3.......3..........6.............9..............13...............18
%C A201539 ..3....9......25.........69...........175.............410..............899
%C A201539 ..3...25.....111........633..........3354...........16393............72811
%C A201539 ..6...69.....633.......7799.........91425..........983981..........9526987
%C A201539 ..9..175....3354......91425.......2446147........61807736.......1408677515
%C A201539 .13..410...16393.....983981......61807736......3762507339.....208164634003
%C A201539 .18..899...72811....9526987....1408677515....208164634003...28456420346436
%C A201539 .24.1859..293831...82847704...28646055184..10298954399450.3505159734744220
%C A201539 .31.3649.1087857..652848538..523398227137.457194210355549
%C A201539 .39.6840.3735546.4712696751.8686880778087
%H A201539 R. H. Hardin, <a href="/A201539/b201539.txt">Table of n, a(n) for n = 1..112</a>
%e A201539 Some solutions for n=3 k=7
%e A201539 ..0..0..0..1..1..2..2....0..1..1..1..2..2..2....0..0..0..1..1..2..2
%e A201539 ..0..0..1..0..0..1..2....0..1..1..2..0..0..2....0..0..2..2..2..2..2
%e A201539 ..0..1..1..0..1..1..2....2..2..2..2..0..1..1....1..1..1..1..2..1..1
%Y A201539 Column 1 is A167614(n-3)
%K A201539 nonn,tabl
%O A201539 1,2
%A A201539 _R. H. Hardin_ Dec 02 2011