A196986 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,4,1,0 for x=0,1,2,3,4

1, 9, 81, 547, 4244, 31791, 242602, 1838579, 13941719, 105949190, 804555155, 6108373537, 46382778115, 352202493024, 2674392958960, 20307546721207, 154201699487668, 1170902185284561, 8891038271677518, 67512544345698850

Offset

1,2

Comments

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

Column 5 of A196989

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +19*a(n-2) +106*a(n-3) +428*a(n-4) +1034*a(n-5) +943*a(n-6) -7692*a(n-7) -40979*a(n-8) -72843*a(n-9) +85062*a(n-10) +406555*a(n-11) +89890*a(n-12) -990937*a(n-13) -1361953*a(n-14) +263139*a(n-15) +2406168*a(n-16) +1755933*a(n-17) -1448065*a(n-18) -4224076*a(n-19) -1491618*a(n-20) +3926178*a(n-21) +10289740*a(n-22) +12379706*a(n-23) +8404440*a(n-24) +2848826*a(n-25) -897343*a(n-26) -8820109*a(n-27) +5130877*a(n-28) -7136789*a(n-29) +1328272*a(n-30) -2705692*a(n-31) +718088*a(n-32) -67176*a(n-33) -199050*a(n-34) +446958*a(n-35) -135708*a(n-36) +195055*a(n-37) -41579*a(n-38) +22729*a(n-39) -8820*a(n-40) -8506*a(n-41) +2496*a(n-42) -880*a(n-43) +870*a(n-44) -129*a(n-45) -26*a(n-46) +a(n-48)

Example

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

Crossrefs

Sequence in context: A214618 A343462 A207009 * A293889 A218268 A223882

Adjacent sequences: A196983 A196984 A196985 * A196987 A196988 A196989

Keyword

nonn

Author

R. H. Hardin Oct 08 2011

Status

approved