A197303 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,4,0,2,1 for x=0,1,2,3,4

3, 23, 98, 639, 3181, 15930, 85087, 450159, 2373372, 12475923, 65599353, 345356968, 1818230847, 9570445721, 50371708666, 265125975409, 1395500272249, 7345271614306, 38661877327141, 203496642084359, 1071104859201058

Offset

1,1

Comments

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

Column 4 of A197307

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +9*a(n-2) +26*a(n-3) +73*a(n-4) +149*a(n-5) -32*a(n-6) -914*a(n-7) -2357*a(n-8) -3867*a(n-9) -3819*a(n-10) +699*a(n-11) +8094*a(n-12) +10668*a(n-13) +6022*a(n-14) -1522*a(n-15) -6309*a(n-16) -4188*a(n-17) -412*a(n-18) +690*a(n-19) -403*a(n-20) -3191*a(n-21) +3126*a(n-22) +15294*a(n-23) +4693*a(n-24) -16594*a(n-25) -14860*a(n-26) -931*a(n-27) +7147*a(n-28) +4489*a(n-29) -1321*a(n-30) +97*a(n-31) +1737*a(n-32) -41*a(n-33) -663*a(n-34) -92*a(n-35) +78*a(n-36) +13*a(n-37) -11*a(n-38) -3*a(n-39) +a(n-40)

Example

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

Crossrefs

Sequence in context: A213846 A301580 A112459 * A039506 A196970 A197557

Adjacent sequences: A197300 A197301 A197302 * A197304 A197305 A197306

Keyword

nonn

Author

R. H. Hardin Oct 13 2011

Status

approved