A252015 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum 1 3 6 or 8 and every diagonal and antidiagonal sum not 1 3 6 or 8

756, 1168, 1168, 1110, 1602, 1110, 1618, 1406, 1406, 1618, 1970, 2002, 1434, 2002, 1970, 2458, 3128, 2170, 2170, 3128, 2458, 3246, 4570, 4770, 3814, 4770, 4570, 3246, 4410, 6562, 8930, 8482, 8482, 8930, 6562, 4410, 5802, 10980, 14450, 16994, 23074

Offset

1,1

Comments

Table starts

..756..1168...1110...1618....1970....2458.....3246.....4410......5802......7874

.1168..1602...1406...2002....3128....4570.....6562....10980.....18568.....26866

.1110..1406...1434...2170....4770....8930....14450....33530.....63546....103410

.1618..2002...2170...3814....8482...16994....29954....67714....136002....239874

.1970..3128...4770...8482...23074...58970...104034...288370....744818...1308322

.2458..4570...8930..16994...58970..159514...303906..1091906...2992258...5688946

.3246..6562..14450..29954..104034..303906...630978..2189170...6377986..13220098

.4410.10980..33530..67714..288370.1091906..2189170..9398338..36100290..71955330

.5802.18568..63546.136002..744818.2992258..6377986.36100290.147443266.312958962

.7874.26866.103410.239874.1308322.5688946.13220098.71955330.312958962.727410882

Links

R. H. Hardin, Table of n, a(n) for n = 1..612

Formula

Empirical for column k:

k=1: [linear recurrence of order 14] for n>22

k=2: [order 15] for n>22

k=3: a(n) = a(n-1) +13*a(n-3) -13*a(n-4) -40*a(n-6) +40*a(n-7) for n>14

k=4: a(n) = a(n-1) +8*a(n-3) -8*a(n-4) for n>12

k=5: a(n) = a(n-1) +21*a(n-3) -21*a(n-4) -104*a(n-6) +104*a(n-7) for n>16

k=6: a(n) = a(n-1) +34*a(n-3) -34*a(n-4) -273*a(n-6) +273*a(n-7) for n>17

k=7: a(n) = a(n-1) +21*a(n-3) -21*a(n-4) for n>15

Example

Some solutions for n=4 k=4
..2..1..3..2..1..0....0..1..2..3..1..2....3..1..2..3..1..2....1..1..1..1..1..1
..0..1..2..0..1..2....2..1..0..2..1..3....2..1..3..2..1..3....1..2..3..1..2..3
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..3..2..1..3..2
..2..1..3..2..1..3....3..1..2..3..1..2....0..1..2..3..1..2....1..1..1..1..1..1
..0..1..2..0..1..2....2..1..3..2..1..3....2..1..3..2..1..0....1..2..3..1..2..0
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..1..1....1..3..2..1..3..2

Crossrefs

Sequence in context: A332879 A256089 A252008 * A108374 A252007 A202198

Adjacent sequences: A252012 A252013 A252014 * A252016 A252017 A252018

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 12 2014

Status

approved