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A240000
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T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
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13
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2, 3, 5, 4, 13, 12, 5, 25, 61, 28, 6, 42, 190, 256, 66, 7, 65, 526, 1372, 1117, 156, 8, 95, 1262, 6527, 10405, 5012, 368, 9, 133, 2766, 27415, 86360, 83029, 22592, 868, 10, 180, 5647, 104291, 635873, 1225281, 685898, 102336, 2048, 11, 237, 10878, 363859
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OFFSET
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1,1
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COMMENTS
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Table starts
....2.......3.........4...........5............6............7............8
....5......13........25..........42...........65...........95..........133
...12......61.......190.........526.........1262.........2766.........5647
...28.....256......1372........6527........27415.......104291.......363859
...66....1117.....10405.......86360.......635873......4267171.....26152051
..156....5012.....83029.....1225281.....15981219....191691132...2090236137
..368...22592....685898....18392485....429788876...9314138750.182333502325
..868..102336...5825700...290513038..12392346376.491124025940
.2048..465662..50417154..4767970186.378942837634
.4832.2123857.441675344.80410934960
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..98
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +2*a(n-3)
k=2: [order 26]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n
n=3: [polynomial of degree 8] for n>6
n=4: [polynomial of degree 19] for n>20
n=5: [polynomial of degree 44] for n>52
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EXAMPLE
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Some solutions for n=4 k=4
..0..3..3..0....0..0..3..3....3..3..0..0....3..3..0..0....0..0..0..0
..0..0..2..1....0..3..2..3....2..2..3..3....0..3..1..3....3..3..0..0
..3..3..0..0....0..0..2..2....2..0..0..0....3..3..1..2....3..3..1..3
..2..1..2..0....0..3..2..3....3..1..0..0....2..2..2..1....3..3..2..2
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CROSSREFS
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Column 1 is A239333
Sequence in context: A131401 A061446 A280690 * A193770 A107476 A094140
Adjacent sequences: A239997 A239998 A239999 * A240001 A240002 A240003
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 30 2014
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STATUS
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approved
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