A197619 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,1,1,1 for x=0,1,2,3,4

0, 0, 27, 98, 242, 863, 3157, 13712, 55965, 202825, 753766, 2893339, 11525072, 44576853, 168309683, 644170650, 2497548575, 9646371371, 37048714857, 142141767377, 546761780936, 2107298815465, 8112374156525, 31185539356744

Offset

1,3

Comments

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

Column 4 of A197623

Links

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

Formula

Empirical: a(n) = 2*a(n-2) +35*a(n-3) +73*a(n-4) +132*a(n-5) -151*a(n-6) -1628*a(n-7) -3858*a(n-8) -3164*a(n-9) +14500*a(n-10) +38136*a(n-11) +38354*a(n-12) -54500*a(n-13) -185382*a(n-14) -106998*a(n-15) -128239*a(n-16) -546331*a(n-17) -1772634*a(n-18) -441963*a(n-19) +6472386*a(n-20) +12393365*a(n-21) +1267839*a(n-22) -10077007*a(n-23) -1840713*a(n-24) +20945699*a(n-25) +25184992*a(n-26) -19820871*a(n-27) -46956209*a(n-28) +19893087*a(n-29) +53217731*a(n-30) +2842210*a(n-31) -10754502*a(n-32) -5041230*a(n-33) +13053780*a(n-34) -2938224*a(n-35) -1474052*a(n-36) +654048*a(n-37) -165728*a(n-38) +136032*a(n-39) -31456*a(n-40) -2112*a(n-41) for n>42

Example

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

Crossrefs

Sequence in context: A154041 A233156 A118615 * A033659 A010015 A256646

Adjacent sequences: A197616 A197617 A197618 * A197620 A197621 A197622

Keyword

nonn

Author

R. H. Hardin Oct 16 2011

Status

approved