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A302877 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302877 #4 Apr 15 2018 10:34:24
%S A302877 1,2,2,3,3,4,5,11,6,8,8,21,17,10,16,13,31,35,37,21,32,21,113,72,95,82,
%T A302877 42,64,34,363,241,306,285,209,86,128,55,813,722,1442,1197,858,536,179,
%U A302877 256,89,1751,1821,5871,7580,4849,2938,1549,370,512,144,5001,4863,21832,41498
%N A302877 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302877 Table starts
%C A302877 ...1...2....3.....5......8.......13........21..........34...........55
%C A302877 ...2...3...11....21.....31......113.......363.........813.........1751
%C A302877 ...4...6...17....35.....72......241.......722........1821.........4863
%C A302877 ...8..10...37....95....306.....1442......5871.......21832........89400
%C A302877 ..16..21...82...285...1197.....7580.....41498......224087......1300510
%C A302877 ..32..42..209...858...4849....45897....359518.....2795440.....24612087
%C A302877 ..64..86..536..2938..23037...320405...3780984....44148194....588417750
%C A302877 .128.179.1549.11126.114810..2489823..44888558...786125894..15974455418
%C A302877 .256.370.4513.44216.603229.20679119.569313013.14827387374.460770487307
%H A302877 R. H. Hardin, <a href="/A302877/b302877.txt">Table of n, a(n) for n = 1..180</a>
%F A302877 Empirical for column k:
%F A302877 k=1: a(n) = 2*a(n-1)
%F A302877 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A302877 k=3: [order 13] for n>16
%F A302877 k=4: [order 56] for n>59
%F A302877 Empirical for row n:
%F A302877 n=1: a(n) = a(n-1) +a(n-2)
%F A302877 n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
%F A302877 n=3: [order 20] for n>21
%F A302877 n=4: [order 60] for n>64
%e A302877 Some solutions for n=5 k=4
%e A302877 ..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..1
%e A302877 ..1..0..1..0. .1..1..1..0. .0..1..0..1. .0..1..1..0. .0..1..0..1
%e A302877 ..1..0..1..0. .1..0..1..0. .0..1..0..1. .1..1..1..1. .0..1..0..1
%e A302877 ..1..0..1..0. .1..0..1..0. .0..1..0..1. .0..1..1..0. .0..0..0..1
%e A302877 ..1..1..0..0. .1..0..0..1. .0..1..0..1. .1..0..1..0. .1..1..0..1
%Y A302877 Column 1 is A000079(n-1).
%Y A302877 Column 2 is A240513.
%Y A302877 Row 1 is A000045(n+1).
%Y A302877 Row 2 is A302310.
%K A302877 nonn,tabl
%O A302877 1,2
%A A302877 _R. H. Hardin_, Apr 15 2018