A197557 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,0,2,2 for x=0,1,2,3,4

3, 23, 106, 927, 4055, 23710, 139477, 791905, 4560098, 25954025, 148624999, 851071784, 4868658595, 27861309921, 159413524406, 912205738931, 5219849087169, 29868491830580, 170911982112069, 977981992958773

Offset

1,1

Comments

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

Column 4 of A197561

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +11*a(n-2) +30*a(n-3) +99*a(n-4) +337*a(n-5) +247*a(n-6) -8*a(n-7) +687*a(n-8) -1525*a(n-9) -6711*a(n-10) -9212*a(n-11) -7726*a(n-12) -2004*a(n-13) +3907*a(n-14) +17248*a(n-15) +12376*a(n-16) +3805*a(n-17) +42013*a(n-18) +26907*a(n-19) +7443*a(n-20) +6529*a(n-21) -40829*a(n-22) -23857*a(n-23) -22159*a(n-24) +7851*a(n-25) +1395*a(n-26) -23643*a(n-27) +30926*a(n-28) +1501*a(n-29) -46607*a(n-30) -17463*a(n-31) +3072*a(n-32) +1311*a(n-33) +9717*a(n-34) +10645*a(n-35) +3739*a(n-36) -864*a(n-37) -1824*a(n-38) +234*a(n-39) +558*a(n-40) -422*a(n-41) +94*a(n-42) +118*a(n-43) -72*a(n-44) -16*a(n-45) +5*a(n-46)

Example

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

Crossrefs

Sequence in context: A197303 A039506 A196970 * A225671 A267816 A269235

Adjacent sequences: A197554 A197555 A197556 * A197558 A197559 A197560

Keyword

nonn

Author

R. H. Hardin Oct 16 2011

Status

approved