A197338 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,2,1,2 for x=0,1,2,3,4

1, 8, 38, 167, 681, 2864, 12148, 51480, 217587, 919656, 3889592, 16451263, 69570928, 294209541, 1244221402, 5261851987, 22252448435, 94105875249, 397975165117, 1683043391582, 7117616634217, 30100509329656, 127295517065791

Offset

1,2

Comments

Every 0 is next to 0 3's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 4 of A197342

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) +20*a(n-3) +4*a(n-4) +35*a(n-5) -46*a(n-6) -60*a(n-7) -128*a(n-8) -147*a(n-9) -159*a(n-10) -62*a(n-11) +278*a(n-12) +293*a(n-13) +293*a(n-14) +171*a(n-15) +423*a(n-16) +459*a(n-17) -301*a(n-18) +83*a(n-19) +364*a(n-20) +29*a(n-21) -778*a(n-22) -694*a(n-23) -591*a(n-24) -383*a(n-25) -31*a(n-26) +509*a(n-27) +628*a(n-28) +202*a(n-29) -163*a(n-30) -154*a(n-31) -32*a(n-32) +16*a(n-33) +8*a(n-34)

Example

Some solutions containing all values 0 to 4 for n=5
..2..2..2..0....0..0..1..0....0..1..0..0....1..1..3..1....0..0..1..0
..2..4..2..0....0..1..3..1....1..3..1..0....3..1..1..0....0..1..3..1
..2..2..2..1....2..2..2..0....0..2..2..2....1..2..2..2....0..2..2..2
..0..1..1..3....2..4..2..0....0..2..4..2....0..2..4..2....0..2..4..2
..1..3..1..1....2..2..2..0....0..2..2..2....0..2..2..2....0..2..2..2

Crossrefs

Sequence in context: A122682 A225429 A123518 * A214931 A229366 A007786

Adjacent sequences: A197335 A197336 A197337 * A197339 A197340 A197341

Keyword

nonn

Author

R. H. Hardin Oct 13 2011

Status

approved