A240364 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4

2, 4, 4, 8, 15, 7, 16, 51, 43, 11, 32, 188, 257, 111, 16, 64, 672, 1693, 1181, 261, 22, 128, 2452, 10997, 13846, 4825, 571, 29, 256, 8822, 74255, 165110, 99412, 18307, 1171, 37, 512, 32077, 492758, 2057843, 2150725, 663122, 64013, 2278, 46, 1024, 115811

Offset

1,1

Comments

Table starts

..2....4.......8........16..........32...........64...........128...........256

..4...15......51.......188.........672.........2452..........8822.........32077

..7...43.....257......1693.......10997........74255........492758.......3349106

.11..111....1181.....13846......165110......2057843......25667276.....329976721

.16..261....4825.....99412.....2150725.....49010279....1144026966...27661711340

.22..571...18307....663122....25831820...1069763402...46251359120.2092454198295

.29.1171...64013...4069449...285724643..21520521111.1718692144996

.37.2278..209366..23273667..2936736845.402124337377

.46.4235..645067.125118158.28324834725

.56.7570.1889163.638885869

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1

k=2: [polynomial of degree 8] for n>4

k=3: [polynomial of degree 26] for n>18

k=4: [polynomial of degree 80] for n>61

Empirical for row n:

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

n=2: [linear recurrence of order 12]

n=3: [order 80]

Example

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

Crossrefs

Column 1 is A000124

Row 1 is A000079

Sequence in context: A069753 A181245 A216950 * A225982 A282528 A297094

Adjacent sequences: A240361 A240362 A240363 * A240365 A240366 A240367

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved