A208085 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

8, 20, 12, 56, 20, 24, 164, 32, 56, 36, 488, 52, 134, 60, 72, 1460, 84, 344, 96, 168, 108, 4376, 136, 888, 156, 402, 180, 216, 13124, 220, 2318, 252, 1032, 288, 504, 324, 39368, 356, 6056, 408, 2664, 468, 1206, 540, 648, 118100, 576, 15848, 660, 6954, 756, 3096

Offset: 1

Author

R. H. Hardin Feb 23 2012

Keywords

• nonn
• tabl

Comments

Table starts

...8..20...56..164..488..1460..4376..13124..39368.118100..354296.1062884

..12..20...32...52...84...136...220....356....576....932....1508....2440

..24..56..134..344..888..2318..6056..15848..41478.108584..284264..744206

..36..60...96..156..252...408...660...1068...1728...2796....4524....7320

..72.168..402.1032.2664..6954.18168..47544.124434.325752..852792.2232618

.108.180..288..468..756..1224..1980...3204...5184...8388...13572...21960

.216.504.1206.3096.7992.20862.54504.142632.373302.977256.2558376.6697854

.324.540..864.1404.2268..3672..5940...9612..15552..25164...40716...65880

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..5596

Crossrefs

Column 1 is A153339(n+2).

Row 1 is A115099.

Row 2 is A022087(n+3).

Row 4 is A022346(n+3).

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-2)

k=2..7: a(n) = 3*a(n-2) for n>3

Empirical for row n:

n=1: a(k)=4*a(k-1)-3*a(k-2)

n=2,4,6: a(k)=a(k-1)+a(k-2)

n=3,5,7: a(k)=3*a(k-1)-3*a(k-3)+a(k-4)