A240376 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 zero plus the sum of the elements diagonally to its northwest, modulo 4

2, 3, 3, 4, 11, 4, 7, 21, 21, 7, 10, 67, 75, 67, 10, 15, 155, 450, 450, 155, 15, 24, 353, 1729, 5161, 1729, 353, 24, 35, 998, 7233, 36398, 36398, 7233, 998, 35, 54, 2256, 36148, 271764, 486179, 271764, 36148, 2256, 54, 83, 5639, 139855, 2492182, 6436979

Offset

1,1

Comments

Table starts

..2.....3.......4..........7...........10............15.............24

..3....11......21.........67..........155...........353............998

..4....21......75........450.........1729..........7233..........36148

..7....67.....450.......5161........36398........271764........2492182

.10...155....1729......36398.......486179.......6436979......110122847

.15...353....7233.....271764......6436979.....169838571.....5145071133

.24...998...36148....2492182....110122847....5145071133...296413962369

.35..2256..139855...17380978...1403151574..121626491919.12947745036751

.54..5639..645733..143489019..20729739995.3384817934297

.83.14624.2919837.1182292032.314460587672

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: [order 15] for n>17

Example

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

Crossrefs

Column 1 is A159288(n+1)

Sequence in context: A293984 A207608 A290818 * A118963 A127641 A328730

Adjacent sequences: A240373 A240374 A240375 * A240377 A240378 A240379

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved