A197086 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,2,0,1 for x=0,1,2,3,4

1, 10, 96, 631, 5101, 37952, 289564, 2200339, 16713718, 127074214, 965583306, 7338942170, 55775566553, 423896532807, 3221643820945, 24484602637498, 186084334450133, 1414249624483974, 10748366775916853, 81688112676072415

Offset

1,2

Comments

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

Column 4 of A197090

Links

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

Formula

Empirical: a(n) = 6*a(n-1) +17*a(n-2) -26*a(n-3) -87*a(n-4) +142*a(n-5) -850*a(n-6) +95*a(n-7) +3242*a(n-8) -2530*a(n-9) +1754*a(n-10) -1012*a(n-11) +3424*a(n-12) -7495*a(n-13) +5596*a(n-14) +1534*a(n-15) -1254*a(n-16) -8051*a(n-17) +3682*a(n-18) -912*a(n-19) -646*a(n-20) +467*a(n-21) +623*a(n-22) -165*a(n-23) -426*a(n-24) +466*a(n-25) -101*a(n-26) +37*a(n-27) +15*a(n-28) -15*a(n-29) +5*a(n-30) for n>31

Example

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

Crossrefs

Sequence in context: A277441 A307021 A197083 * A278359 A125945 A259497

Adjacent sequences: A197083 A197084 A197085 * A197087 A197088 A197089

Keyword

nonn

Author

R. H. Hardin Oct 10 2011

Status

approved