A117374 -id:A117374 - cp's OEIS frontend

A197475 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

1, 1, 1, 3, 2, 3, 1, 6, 6, 1, 4, 12, 26, 12, 4, 4, 24, 46, 46, 24, 4, 5, 50, 181, 184, 181, 50, 5, 8, 98, 374, 748, 748, 374, 98, 8, 9, 194, 1300, 2824, 5408, 2824, 1300, 194, 9, 13, 394, 2886, 10934, 22672, 22672, 10934, 2886, 394, 13, 17, 786, 9446, 42474, 151748

Offset: 1

R. H. Hardin Oct 15 2011

Every 0 is next to 0 0's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's
Table starts
..1...1.....3......1........4.........4...........5............8..............9
..1...2.....6.....12.......24........50..........98..........194............394
..3...6....26.....46......181.......374........1300.........2886...........9446
..1..12....46....184......748......2824.......10934........42474.........164782
..4..24...181....748.....5408.....22672......151748.......684002........4368923
..4..50...374...2824....22672....165200.....1265828......9507212.......72145488
..5..98..1300..10934...151748...1265828....16544206....145244408.....1830370547
..8.194..2886..42474...684002...9507212...145244408...2117012786....31678990290
..9.394..9446.164782..4368923..72145488..1830370547..31678990290...779857304215
.13.786.22060.638460.20344854.544829612.16537658774.466669377276.13814430334490

			Some solutions containing all values 0 to 4 for n=6 k=4
..0..3..0..2....2..0..3..0....0..3..0..2....2..0..2..1....1..1..2..0
..2..0..4..0....0..3..0..3....1..0..4..0....0..4..0..1....0..2..0..1
..1..1..0..2....2..1..3..0....1..3..0..3....2..0..1..0....1..1..2..1
..2..0..3..1....0..1..0..3....2..0..3..0....1..2..1..2....0..3..0..2
..0..3..0..1....2..0..4..0....0..1..1..2....1..0..3..0....3..0..4..0
..1..1..2..0....1..1..0..2....2..0..2..0....0..3..0..2....0..3..0..2

R. H. Hardin, Table of n, a(n) for n = 1..241

Column 1 is A117374(n-2)

A117372 Riordan array (1-3x,x(1-x)).

Original entry on oeis.org

1, -3, 1, 0, -4, 1, 0, 3, -5, 1, 0, 0, 7, -6, 1, 0, 0, -3, 12, -7, 1, 0, 0, 0, -10, 18, -8, 1, 0, 0, 0, 3, -22, 25, -9, 1, 0, 0, 0, 0, 13, -40, 33, -10, 1, 0, 0, 0, 0, -3, 35, -65, 42, -11, 1, 0, 0, 0, 0, 0, -16, 75, -98, 52, -12, 1

Offset: 0

Paul Barry, Mar 10 2006

Row sums are A117373. Diagonal sums are A117374. Inverse is A117375.

			Triangle begins
1,
-3, 1,
0, -4, 1,
0, 3, -5, 1,
0, 0, 7, -6, 1,
0, 0, -3, 12, -7, 1,
0, 0, 0, -10, 18, -8, 1,
0, 0, 0, 3, -22, 25, -9, 1

Number triangle T(n,k)=(-1)^(n-k)(C(k,n-k)+3*C(k, n-k-1))

cp's OEIS Frontend

A197475 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs