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A188553 T(n,k) = Number of n X k binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally. 8
2, 3, 3, 4, 5, 4, 5, 8, 7, 5, 6, 12, 12, 9, 6, 7, 17, 20, 16, 11, 7, 8, 23, 32, 28, 20, 13, 8, 9, 30, 49, 48, 36, 24, 15, 9, 10, 38, 72, 80, 64, 44, 28, 17, 10, 11, 47, 102, 129, 112, 80, 52, 32, 19, 11, 12, 57, 140, 201, 192, 144, 96, 60, 36, 21, 12, 13, 68, 187, 303, 321, 256, 176 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

..2..3..4..5...6...7...8...9...10...11...12....13....14....15....16.....17

..3..5..8.12..17..23..30..38...47...57...68....80....93...107...122....138

..4..7.12.20..32..49..72.102..140..187..244...312...392...485...592....714

..5..9.16.28..48..80.129.201..303..443..630...874..1186..1578..2063...2655

..6.11.20.36..64.112.192.321..522..825.1268..1898..2772..3958..5536...7599

..7.13.24.44..80.144.256.448..769.1291.2116..3384..5282..8054.12012..17548

..8.15.28.52..96.176.320.576.1024.1793.3084..5200..8584.13866.21920..33932

..9.17.32.60.112.208.384.704.1280.2304.4097..7181.12381.20965.34831..56751

.10.19.36.68.128.240.448.832.1536.2816.5120..9217.16398.28779.49744..84575

.11.21.40.76.144.272.512.960.1792.3328.6144.11264.20481.36879.65658.115402

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..9934

FORMULA

Empirical: T(n,k) = (n+1)*2^(k-1) + (1-k)*2^(k-2) for k<n+3, and then the entire row n is a polynomial of degree n in k.

EXAMPLE

Some solutions for 5X3

..1..1..1....1..0..0....0..0..0....1..1..1....1..1..1....1..1..1....1..1..1

..1..1..1....0..0..0....0..0..0....1..1..1....1..1..1....1..1..1....1..1..1

..1..1..1....0..0..0....0..0..0....1..1..1....1..0..0....1..1..0....1..1..1

..1..1..1....0..0..0....0..0..0....1..1..0....0..0..0....1..0..0....1..1..1

..1..1..1....0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....1..1..0

MAPLE

# (Empirical)

T:= (n, k)-> `if`(k<=n+1, (2*n+3-k)*2^(k-2), (n+1-k)*binomial(k-1, n) * add(binomial(n, j-1)/(k-j)*T(n, j)*(-1)^(n-j), j=1..n+1)): seq(seq(T(n, 1+d-n), n=1..d), d=1..15);

CROSSREFS

Diagonal is A045623.

Column 4 is A086570.

Row 2 is A022856(n+4).

Upper diagonals T(n,n+i) for i=1..8 give: A001792, A001787(n+1), A000337(n+1), A045618, A045889, A034009, A055250, A055251.

Lower diagonals T(n+i,n) for i=1..7 give: A045891(n+1), A034007(n+2), A111297(n+1), A159694(n-1), A159695(n-1), A159696(n-1), A159697(n-1).

Antidiagonal sums give A065220(n+5).

Sequence in context: A321440 A115729 A115728 * A335680 A026354 A179840

Adjacent sequences:  A188550 A188551 A188552 * A188554 A188555 A188556

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Maple program from Alois P. Heinz in the Sequence Fans Mailing List, Apr 04 2011

EXTENSIONS

More references from Alois P. Heinz, Apr 11 2011

STATUS

approved

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Last modified August 3 17:26 EDT 2020. Contains 336200 sequences. (Running on oeis4.)