A197499 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,1,1,0 for x=0,1,2,3,4

1, 9, 53, 181, 967, 4447, 20411, 99367, 473509, 2249979, 10740561, 51245685, 244406613, 1165674879, 5559988993, 26520385505, 126494970513, 603345410731, 2877810161871, 13726438785461, 65471603280973, 312282907797439

Offset

1,2

Comments

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

Column 4 of A197503

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) +32*a(n-3) +27*a(n-4) -9*a(n-5) -247*a(n-6) -328*a(n-7) -85*a(n-8) +728*a(n-9) +737*a(n-10) -15*a(n-11) -1292*a(n-12) -269*a(n-13) +454*a(n-14) +1157*a(n-15) -718*a(n-16) -314*a(n-17) -196*a(n-18) +2441*a(n-19) +3336*a(n-20) +415*a(n-21) -2431*a(n-22) -4715*a(n-23) -1425*a(n-24) -713*a(n-25) +460*a(n-26) +312*a(n-27) +210*a(n-28) -799*a(n-29) +249*a(n-30) -50*a(n-31) -545*a(n-32) -486*a(n-33) +88*a(n-34) +252*a(n-35) +204*a(n-36) +152*a(n-37) +64*a(n-38) +25*a(n-39) +27*a(n-40) +19*a(n-41) +2*a(n-42) -a(n-43)

Example

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

Crossrefs

Sequence in context: A344820 A156544 A094793 * A036425 A126085 A055854

Adjacent sequences: A197496 A197497 A197498 * A197500 A197501 A197502

Keyword

nonn

Author

R. H. Hardin Oct 15 2011

Status

approved