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A207453 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically 11
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 23 20:29 EDT 2022. Contains 353993 sequences. (Running on oeis4.)