A239849 T(n,k)=Number of nXk 0..3 arrays with no element equal to one 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

2, 3, 3, 4, 8, 4, 5, 17, 17, 5, 6, 35, 68, 35, 6, 7, 64, 244, 244, 64, 7, 8, 109, 777, 1613, 777, 109, 8, 9, 176, 2221, 9066, 9066, 2221, 176, 9, 10, 272, 5853, 46260, 94613, 46260, 5853, 272, 10, 11, 405, 14488, 214126, 874352, 874352, 214126, 14488, 405, 11, 12

Offset

1,1

Comments

Table starts

..2...3.....4........5..........6...........7............8............9

..3...8....17.......35.........64.........109..........176..........272

..4..17....68......244........777........2221.........5853........14488

..5..35...244.....1613.......9066.......46260.......214126.......921674

..6..64...777.....9066......94613......874352......7359682.....57010666

..7.109..2221....46260.....874352....15039319....232886648...3315673203

..8.176..5853...214126....7359682...232886648...6712505927.177152281120

..9.272.14488...921674...57010666..3315673203.177152281120

.10.405.34057..3745690..415293446.44101959522

.11.584.76495.14493362.2875073417

Links

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

Formula

Empirical for column k:

k=1: a(n) = n + 1

k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (53/12)*n - 6 for n>2

k=3: [polynomial of degree 13] for n>9

k=4: [polynomial of degree 40] for n>31

k=5: [polynomial of degree 121] for n>98

Example

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

Crossrefs

Sequence in context: A238812 A227269 A156353 * A202560 A227165 A173933

Adjacent sequences: A239846 A239847 A239848 * A239850 A239851 A239852

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 28 2014

Status

approved