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A239858 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4 14
2, 2, 2, 4, 3, 4, 6, 9, 5, 6, 8, 12, 44, 4, 8, 14, 29, 78, 84, 5, 14, 20, 63, 255, 203, 130, 5, 20, 30, 100, 742, 1114, 484, 343, 6, 30, 48, 215, 1382, 3463, 4549, 1757, 685, 10, 48, 70, 468, 5647, 9963, 19065, 28184, 4979, 1704, 11, 70, 108, 785, 14755, 71695, 77212 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
..2..2....4......6........8........14.........20..........30.........48
..2..3....9.....12.......29........63........100.........215........468
..4..5...44.....78......255.......742.......1382........5647......14755
..6..4...84....203.....1114......3463.......9963.......71695.....219708
..8..5..130....484.....4549.....19065......77212......970717....4024283
.14..5..343...1757....28184....176208.....937154....23072270..141040759
.20..6..685...4979...125255...1162638....9885999...421824199.5282952362
.30.10.1704..19850...860559..11924924..147826427.14757679494
.48.11.3977..68830..4802971.111900643.2030390429
.70.15.7958.207822.24477675.995175724
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: a(n) = a(n-2) +a(n-5) for n>9
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 17] for n>21
EXAMPLE
Some solutions for n=4 k=4
..3..2..3..3....2..3..3..2....2..3..3..3....3..2..2..2....2..3..2..2
..2..1..1..2....3..1..1..3....3..1..1..2....2..1..0..0....3..1..1..0
..3..0..2..2....3..1..1..2....3..2..2..2....3..1..3..0....2..1..2..0
..3..2..0..0....2..3..0..2....2..3..0..0....2..3..3..3....2..0..0..3
CROSSREFS
Sequence in context: A241164 A029157 A247301 * A031437 A282561 A237598
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 28 2014
STATUS
approved

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Last modified April 15 14:58 EDT 2024. Contains 371692 sequences. (Running on oeis4.)