A207453 T(n,k) = Number of n X k 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 90, 64, 10, 26, 256, 330, 168, 100, 12, 42, 676, 1008, 760, 270, 144, 14, 68, 1764, 3354, 2560, 1450, 396, 196, 16, 110, 4624, 10710, 10088, 5200, 2460, 546, 256, 18, 178, 12100, 34884, 36456, 23530, 9216, 3850, 720

Offset

1,1

Comments

Table starts

..2...4...6...10....16.....26.....42......68......110......178.......288

..4..16..36..100...256....676...1764....4624....12100....31684.....82944

..6..36..90..330..1008...3354..10710...34884...112530...364722...1179360

..8..64.168..760..2560..10088..36456..138176...509960..1910296...7096320

.10.100.270.1450..5200..23530..92610..396100..1610950..6754210..27799200

.12.144.396.2460..9216..46956.196812..932688..4086060.18819228..83939328

.14.196.546.3850.14896..84266.370734.1922564..8935850.44655394.212625504

.16.256.720.5680.22528.139984.640080.3599104.17556880.94358512.474439680

Links

R. H. Hardin, Table of n, a(n) for n = 1..1573

Formula

Empirical for column k:

k=1: a(n) = 2*n;

k=2: a(n) = 4*n^2;

k=3: a(n) = 12*n^2 - 6*n;

k=4: a(n) = 10*n^3 + 10*n^2 - 10*n;

k=5: a(n) = 48*n^3 - 32*n^2;

k=6: a(n) = 26*n^4 + 78*n^3 - 104*n^2 + 26*n;

k=7: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n;

k=8: a(n) = 68*n^5 + 408*n^4 - 612*n^3 + 204*n^2;

k=9: a(n) = 550*n^5 - 990*n^3 + 660*n^2 - 110*n;

k=10: a(n) = 178*n^6 + 1780*n^5 - 2670*n^4 + 534*n^3 + 534*n^2 - 178*n;

k=11: a(n) = 1728*n^6 + 1440*n^5 - 6912*n^4 + 5184*n^3 - 1152*n^2;

k=12: a(n) = 466*n^7 + 6990*n^6 - 9320*n^5 - 2796*n^4 + 8388*n^3 - 3728*n^2 + 466*n;

k=13: a(n) = 5278*n^7 + 10556*n^6 - 36946*n^5 + 27144*n^4 - 3016*n^3 - 3016*n^2 + 754*n;

k=14: a(n) = 1220*n^8 + 25620*n^7 - 25620*n^6 - 42700*n^5 + 73200*n^4 - 36600*n^3 + 6100*n^2;

k=15: a(n) = 15792*n^8 + 55272*n^7 - 165816*n^6 + 98700*n^5 + 39480*n^4 - 59220*n^3 + 19740*n^2 - 1974*n.

Empirical for row n:

n=1: a(k)=a(k-1)+a(k-2);

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

n=3: a(k)=a(k-1)+7*a(k-2)+2*a(k-3)-4*a(k-4);

n=4: a(k)=a(k-1)+10*a(k-2)+3*a(k-3)-9*a(k-4);

n=5: a(k)=a(k-1)+13*a(k-2)+4*a(k-3)-16*a(k-4);

n=6: a(k)=a(k-1)+16*a(k-2)+5*a(k-3)-25*a(k-4);

n=7: a(k)=a(k-1)+19*a(k-2)+6*a(k-3)-36*a(k-4);

apparently for row n>2: a(k)=a(k-1)+(3*n-2)*a(k-2)+(n-1)*a(k-3)+(n-1)^2*a(k-4).

Example

Some solutions for n=5, k=3
..1..0..1....1..1..0....1..1..1....0..1..1....0..1..0....0..1..0....0..1..1
..1..0..1....1..0..0....0..1..1....0..1..1....0..1..1....1..0..0....1..0..1
..1..0..1....1..0..0....0..1..0....0..1..0....0..1..1....1..0..0....1..0..1
..1..0..1....1..0..0....0..1..0....0..1..0....0..1..0....1..0..0....1..0..1
..1..0..0....1..0..0....0..1..0....0..1..0....0..1..0....1..0..0....1..0..1

Crossrefs

Column 2 is A016742.

Column 3 is A152746.

Row 1 is A006355(n+2).

Row 2 is A206981.

Sequence in context: A207928 A207858 A208379 * A208287 A208501 A207589

Adjacent sequences: A207450 A207451 A207452 * A207454 A207455 A207456

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2012

Status

approved