A196782 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,3,0,1 for x=0,1,2,3,4.

1, 7, 39, 145, 797, 3569, 17175, 81389, 385231, 1829101, 8668831, 41113007, 194955001, 924449179, 4383753391, 20787435021, 98573175383, 467429309303, 2216527199343, 10510668481659, 49841089379745, 236344089239897

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

Column 4 of A196786.

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) +15*a(n-3) -a(n-4) -6*a(n-5) -28*a(n-6) -14*a(n-7) +13*a(n-8) -13*a(n-9) +3*a(n-10).

Empirical g.f.: x*(1 + 5*x + 15*x^2 - 18*x^3 + 13*x^4 - 47*x^5 + x^6 - 17*x^7 + 12*x^8 + 3*x^9) / (1 - 2*x - 10*x^2 - 15*x^3 + x^4 + 6*x^5 + 28*x^6 + 14*x^7 - 13*x^8 + 13*x^9 - 3*x^10). - Colin Barker, May 09 2018

Example

Some solutions for n=5:
..0..3..0..0....0..3..0..0....0..0..3..0....0..0..3..0....0..0..0..0
..3..0..0..3....0..0..0..0....0..0..0..0....0..3..0..3....0..3..0..0
..0..3..0..0....3..0..0..0....3..0..0..0....0..3..0..0....0..1..0..0
..0..3..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..4..1..0
..0..0..3..0....0..3..0..0....0..0..0..0....0..3..0..0....0..1..0..0

Crossrefs

Cf. A196786.

Sequence in context: A373539 A027482 A352310 * A128554 A225617 A032207

Adjacent sequences: A196779 A196780 A196781 * A196783 A196784 A196785

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved