A251236 T(n,k) = Number of (n+1) X (k+1) 0..3 arrays with every 2 X 2 subblock summing to 6 and no 2 X 2 subblock having exactly two nonzero entries.

38, 110, 110, 322, 270, 322, 966, 694, 694, 966, 2930, 1870, 1592, 1870, 2930, 8982, 5194, 3886, 3886, 5194, 8982, 27714, 14786, 9914, 8686, 9914, 14786, 27714, 85958, 42850, 26224, 20490, 20490, 26224, 42850, 85958, 267602, 125934, 71322, 50570

Offset

1,1

Comments

Table starts:

.....38.....110.....322.....966....2930....8982....27714....85958...267602

....110.....270.....694....1870....5194...14786....42850...125934...374166

....322.....694....1592....3886....9914...26224....71322...198318...561212

....966....1870....3886....8686...20490...50570...129378...340782...918878

...2930....5194....9914...20490...44966..103926...250622...626122..1610186

...8982...14786...26224...50570..103926..225936...514950..1222090..3000620

..27714...42850...71322..129378..250622..514950..1112526..2511890..5892002

..85958..125934..198318..340782..626122.1222090..2511890..5407182.12127278

.267602..374166..561212..918878.1610186.3000620..5892002.12127278

.835574.1121566.1611002.2525262.4240330.7579486.14279706

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k (k=3 recurrence works also for k=1 and k=2):

k=1: a(n) = 7*a(n-1) -12*a(n-2) -8*a(n-3) +24*a(n-4)

k=2: [order 9]

k=3: [order 11]

k=4: [same order 11]

k=5: [same order 11]

k=6: [same order 11]

k=7: [same order 11]

Example

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

Crossrefs

Sequence in context: A044225 A044606 A244177 * A283804 A251229 A282850

Adjacent sequences: A251233 A251234 A251235 * A251237 A251238 A251239

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved