A196074 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,2,1,4 for x=0,1,2,3,4

0, 0, 1, 8, 39, 60, 111, 343, 861, 2115, 5016, 13734, 35912, 82715, 202744, 522390, 1333539, 3288827, 8106150, 20528101, 51563620, 128020497, 319184841, 801237793, 2009081101, 5009247370, 12506463250, 31323071350, 78380580569, 195823809542

Offset

1,4

Comments

Every 0 is next to 0 0'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 4's

Column 4 of A196078

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-2) +4*a(n-3) +14*a(n-4) +23*a(n-5) -2*a(n-6) +24*a(n-7) +44*a(n-8) -133*a(n-9) -186*a(n-10) -317*a(n-11) -363*a(n-12) +372*a(n-13) +825*a(n-14) -50*a(n-15) -513*a(n-16) +173*a(n-17) +42*a(n-18) +441*a(n-19) +835*a(n-20) +563*a(n-21) +336*a(n-22) -1995*a(n-23) -4044*a(n-24) -1095*a(n-25) +4154*a(n-26) +1656*a(n-27) -395*a(n-28) +3391*a(n-29) -709*a(n-30) -3210*a(n-31) -1608*a(n-32) -2382*a(n-33) -47*a(n-34) -219*a(n-35) +91*a(n-36) +1032*a(n-37)

Example

Some solutions for n=5
..0..1..3..1....1..0..2..2....2..2..2..0....2..2..0..1....0..2..2..2
..1..0..1..1....3..1..2..2....2..1..2..2....2..2..1..3....2..2..1..2
..3..1..1..3....1..1..1..0....2..3..1..2....0..1..0..1....2..1..3..2
..1..0..1..1....1..3..3..1....2..1..2..2....1..3..2..2....2..0..1..2
..0..1..3..1....0..1..1..0....2..2..2..0....0..1..2..2....2..2..2..2

Crossrefs

Sequence in context: A229366 A007786 A026662 * A329172 A346326 A003353

Adjacent sequences: A196071 A196072 A196073 * A196075 A196076 A196077

Keyword

nonn

Author

R. H. Hardin Sep 27 2011

Status

approved