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A240364
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 two plus the sum of the elements diagonally to its northwest, modulo 4
11
2, 4, 4, 8, 15, 7, 16, 51, 43, 11, 32, 188, 257, 111, 16, 64, 672, 1693, 1181, 261, 22, 128, 2452, 10997, 13846, 4825, 571, 29, 256, 8822, 74255, 165110, 99412, 18307, 1171, 37, 512, 32077, 492758, 2057843, 2150725, 663122, 64013, 2278, 46, 1024, 115811
OFFSET
1,1
COMMENTS
Table starts
..2....4.......8........16..........32...........64...........128...........256
..4...15......51.......188.........672.........2452..........8822.........32077
..7...43.....257......1693.......10997........74255........492758.......3349106
.11..111....1181.....13846......165110......2057843......25667276.....329976721
.16..261....4825.....99412.....2150725.....49010279....1144026966...27661711340
.22..571...18307....663122....25831820...1069763402...46251359120.2092454198295
.29.1171...64013...4069449...285724643..21520521111.1718692144996
.37.2278..209366..23273667..2936736845.402124337377
.46.4235..645067.125118158.28324834725
.56.7570.1889163.638885869
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
k=2: [polynomial of degree 8] for n>4
k=3: [polynomial of degree 26] for n>18
k=4: [polynomial of degree 80] for n>61
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: [linear recurrence of order 12]
n=3: [order 80]
EXAMPLE
Some solutions for n=4 k=4
..0..0..0..3....3..3..0..0....0..3..3..0....0..0..0..0....0..0..0..0
..3..3..0..0....3..3..0..0....0..0..0..3....0..3..1..3....0..3..1..0
..3..2..0..3....3..2..3..3....0..0..0..2....3..3..2..0....3..3..0..1
..3..2..0..3....0..3..2..0....3..3..0..0....0..3..3..2....3..3..0..0
CROSSREFS
Column 1 is A000124
Row 1 is A000079
Sequence in context: A069753 A181245 A216950 * A225982 A282528 A297094
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 04 2014
STATUS
approved