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A240394 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4 11
1, 1, 2, 1, 5, 2, 1, 7, 12, 4, 1, 9, 32, 50, 4, 1, 11, 62, 258, 120, 8, 1, 13, 118, 954, 1232, 493, 8, 1, 15, 206, 3064, 8656, 10291, 1184, 16, 1, 17, 351, 9075, 50756, 142016, 48826, 4863, 16, 1, 19, 568, 27120, 263816, 1568581, 1314136, 405404, 11684, 32, 1, 21, 882 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts
..1.....1........1..........1............1.............1.............1
..2.....5........7..........9...........11............13............15
..2....12.......32.........62..........118...........206...........351
..4....50......258........954.........3064..........9075.........27120
..4...120.....1232.......8656........50756........263816.......1378418
..8...493....10291.....142016......1568581......14958462.....138422394
..8..1184....48826....1314136.....27938412.....502139307....8505203924
.16..4863...405404...21792634....910553970...31597696508.1003858789731
.16.11684..1922824..202647943..16647316316.1127672103190
.32.47994.15957927.3370994234.551914186148
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-2)
k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
k=3: [order 48] for n>49
Empirical for row n:
n=1: a(n) = 1
n=2: a(n) = 2*n + 1 for n>1
n=3: a(n) = (1/6)*n^4 - (5/6)*n^3 + (13/3)*n^2 + (31/3)*n - 48 for n>5
n=4: [polynomial of degree 14] for n>13
n=5: [polynomial of degree 44] for n>38
EXAMPLE
Some solutions for n=4 k=4
..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0
..1..0..3..3....1..0..0..3....1..3..3..0....1..0..0..0....3..2..0..0
..3..0..2..2....3..0..2..3....3..1..3..2....3..0..2..0....1..2..2..3
..3..0..1..1....1..3..2..0....1..2..2..2....3..0..2..0....3..2..2..2
CROSSREFS
Column 1 is A016116
Sequence in context: A134566 A128694 A088421 * A259447 A228823 A249756
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 04 2014
STATUS
approved

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Last modified June 23 15:01 EDT 2024. Contains 373651 sequences. (Running on oeis4.)