A240250 T(n,k)=Number of nXk 0..3 arrays with no element equal to the sum of elements to its left or the sum of the elements above it or the sum of the elements diagonally to its northwest or the sum of the elements antidiagonally to its northeast, modulo 4

3, 6, 6, 14, 0, 14, 32, 8, 0, 32, 72, 40, 16, 0, 72, 164, 152, 162, 44, 0, 164, 372, 540, 688, 536, 122, 0, 372, 844, 1578, 3964, 3530, 2152, 368, 0, 844, 1916, 5912, 16600, 33216, 17476, 8564, 1058, 0, 1916, 4348, 18528, 110134, 189430, 246458, 96752, 29708, 3088

Offset

1,1

Comments

Table starts

....3.6....14......32.......72........164........372.........844........1916

....6.0.....8......40......152........540.......1578........5912.......18528

...14.0....16.....162......688.......3964......16600......110134......492060

...32.0....44.....536.....3530......33216.....189430.....2166204....14671432

...72.0...122....2152....17476.....246458....2077950....38186418...396423206

..164.0...368....8564....96752....2043488...26986182...807290260.13612747250

..372.0..1058...29708...508444...16426440..326181996.16596832788

..844.0..3088..111370..2779754..143288058.4661555368

.1916.0..8534..400694.15042466.1177286938

.4348.0.24012.1443716.82159256

Links

R. H. Hardin, Table of n, a(n) for n = 1..109

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) for n>2

Empirical for row n:

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

n=2: [order 25]

Example

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

Crossrefs

Row and column 1 are A238768

Sequence in context: A208796 A319867 A202931 * A239424 A119306 A107972

Adjacent sequences: A240247 A240248 A240249 * A240251 A240252 A240253

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 03 2014

Status

approved