A199909 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).

1, 1, 2, 1, 4, 6, 1, 4, 12, 8, 1, 6, 24, 24, 14, 1, 8, 42, 72, 82, 32, 1, 8, 60, 152, 256, 232, 56, 1, 10, 84, 256, 804, 1312, 654, 100, 1, 12, 114, 448, 1836, 5016, 5206, 2044, 204, 1, 12, 144, 680, 3196, 12872, 24864, 21208, 6096, 388, 1, 14, 180, 952, 6064, 29864, 77874

Offset: 1

Author

R. H. Hardin Nov 11 2011

Keywords

• nonn
• tabl

Comments

Table starts

...1.....1......1.......1........1.........1.........1..........1..........1

...2.....4......4.......6........8.........8........10.........12.........12

...6....12.....24......42.......60........84.......114........144........180

...8....24.....72.....152......256.......448.......680........952.......1384

..14....82....256.....804.....1836......3196......6064......10276......14846

..32...232...1312....5016....12872.....29864.....62776.....114768.....200520

..56...654...5206...24864....77874....216530....518560....1071202....2114394

.100..2044..21208..139148...547604...1699268...4854740...11588992...24551100

.204..6096..97668..814776..3784512..14546928..47329800..125461824..306360336

.388.18564.422052.4509164.25525476.116482068.436295060.1308549932.3582143596

Examples

			Some solutions for n=7 k=6
.-6...-3....4...-6...-3....4....4...-6....4....3....0....3...-6...-6....0....4
.-4....2....2...-4...-4....3...-1...-1....5....2....4....4....4....5...-1...-6
..4...-5....0...-3...-3....1....0....3...-5....4....0...-3...-6...-3...-5....4
.-4....6...-1....5....2...-6...-2....1...-4....0...-2...-1....1....1....0...-1
..6....5....0....4....3....5...-6...-1...-6...-4...-4...-5...-1...-4...-2....0
.-2...-6....1....6....5...-3....2....6....2...-3....6....5....6....1....6...-4
..6....1...-6...-2....0...-4....3...-2....4...-2...-4...-3....2....6....2....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..871

Crossrefs

Column 1 is A199697

Row 2 is A063200(n+2)

Formula

Empirical for rows:

T(1,k)=1

T(2,k)=a(k-1)+a(k-3)-a(k-4)

T(3,k)=2*a(k-1)-a(k-2)+a(k-3)-2*a(k-4)+a(k-5)

T(4,k)=a(k-1)+3*a(k-3)-3*a(k-4)-3*a(k-6)+3*a(k-7)+a(k-9)-a(k-10)

T(5,k)=a(k-1)+4*a(k-3)-4*a(k-4)-6*a(k-6)+6*a(k-7)+4*a(k-9)-4*a(k-10)-a(k-12)+a(k-13)

T(6,k)=2*a(k-1)-a(k-2)+4*a(k-3)-8*a(k-4)+4*a(k-5)-6*a(k-6)+12*a(k-7)-6*a(k-8)+4*a(k-9)-8*a(k-10)+4*a(k-11)-a(k-12)+2*a(k-13)-a(k-14)

T(7,k)=a(k-1)+6*a(k-3)-6*a(k-4)-15*a(k-6)+15*a(k-7)+20*a(k-9)-20*a(k-10)-15*a(k-12)+15*a(k-13)+6*a(k-15)-6*a(k-16)-a(k-18)+a(k-19)