A240406 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 4

1, 2, 2, 3, 5, 3, 4, 14, 14, 4, 7, 24, 77, 24, 7, 10, 77, 235, 235, 77, 10, 15, 182, 1381, 1304, 1381, 182, 15, 24, 397, 5566, 13648, 13648, 5566, 397, 24, 35, 1164, 21413, 98837, 257243, 98837, 21413, 1164, 35, 54, 2626, 114951, 692520, 3366314, 3366314, 692520

Offset

1,2

Comments

Table starts

..1....2.......3.........4............7............10............15

..2....5......14........24...........77...........182...........397

..3...14......77.......235.........1381..........5566.........21413

..4...24.....235......1304........13648.........98837........692520

..7...77....1381.....13648.......257243.......3366314......43820839

.10..182....5566.....98837......3366314......80283637....1935005419

.15..397...21413....692520.....43820839....1935005419...85908009949

.24.1164..114951...6686074....766539340...62076655091.5128168982319

.35.2626..447479..47001423...9754760605.1450984782112

.54.6439.1942846.368795251.139442821024

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = a(n-2) +2*a(n-3)

k=2: [order 15]

Example

Some solutions for n=4 k=4
..2..1..1..2....2..2..2..2....2..1..2..1....2..2..2..1....2..2..2..1
..3..1..3..3....3..3..0..0....3..3..0..1....3..3..0..1....3..3..0..1
..2..0..0..1....2..2..0..0....2..2..0..0....2..2..2..0....2..2..0..0
..3..3..2..2....3..1..0..2....3..3..0..0....3..3..0..0....3..1..0..3

Crossrefs

Column 1 is A159288

Sequence in context: A196729 A197069 A197450 * A303682 A304133 A303808

Adjacent sequences: A240403 A240404 A240405 * A240407 A240408 A240409

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved