A197369 Number of n X 4 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,4,1,0,1 for x=0,1,2,3,4.

1, 7, 45, 161, 899, 4023, 19387, 92169, 436539, 2077281, 9861263, 46848707, 222547181, 1057107041, 5021579939, 23853406065, 113308835575, 538241104209, 2556757711375, 12145141483565, 57691981461499, 274049091332625

Offset

1,2

Comments

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

Column 4 of A197373.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +10*a(n-2) +18*a(n-3) -7*a(n-4) -33*a(n-5) -58*a(n-6) +13*a(n-7) +22*a(n-8) -31*a(n-9) +18*a(n-10) -3*a(n-11).

Empirial: G.f.: -x*(-1 -5*x -21*x^2 +17*x^3 -8*x^4 +113*x^5 -57*x^6 +12*x^7 -20*x^8 -5*x^9 +5*x^10)/(1-2*x -10*x^2 -18*x^3 +7*x^4 +33*x^5 +58*x^6 -13*x^7 -22*x^8 +31*x^9 -18*x^10 +3*x^11) . - R. J. Mathar, Aug 27 2024

Example

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

Crossrefs

Cf. A197373.

Sequence in context: A212105 A208826 A206808 * A059937 A278682 A342568

Adjacent sequences: A197366 A197367 A197368 * A197370 A197371 A197372

Keyword

nonn

Author

R. H. Hardin Oct 14 2011

Status

approved