A197051 Number of nX5 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.

4, 10, 38, 108, 358, 1132, 3580, 11382, 36270, 114992, 365628, 1162290, 3692624, 11733828, 37293892, 118504546, 376583590, 1196750110, 3803034578, 12085297922, 38405269512, 122045123484, 387837623386, 1232482503260, 3916616317912

Offset

1,1

Comments

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

Column 5 of A197054.

Links

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

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +10*a(n-3) +4*a(n-4) -20*a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) -16*a(n-9) +4*a(n-10) +a(n-13) for n>14.

Equivalent empirical g.f.: 4*x - 2*x^2*(5+14*x+15*x^2-x^3-39*x^4-8*x^5+6*x^6-21*x^7-13*x^8-x^9+x^10+3*x^11+3*x^12) / ( -1+x+4*x^2+10*x^3+4*x^4-20*x^5+x^6-2*x^7+2*x^8-16*x^9+4*x^10+x^13 ). - R. J. Mathar, Oct 10 2011

Example

Some solutions for n=4
..0..1..2..0..2....1..1..0..3..0....0..3..0..3..0....0..2..1..0..2
..2..1..0..4..0....0..2..2..0..3....3..0..3..0..2....2..0..2..2..0
..0..1..3..0..3....3..0..2..2..0....0..2..1..1..1....1..2..0..2..1
..1..1..0..3..0....0..3..0..1..1....1..1..0..2..0....0..1..2..0..1

Crossrefs

Sequence in context: A046562 A240382 A220198 * A149191 A149192 A032123

Adjacent sequences: A197048 A197049 A197050 * A197052 A197053 A197054

Keyword

nonn

Author

R. H. Hardin, Oct 09 2011

Status

approved