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A188824 T(n,k)=Number of nXk binary arrays without the pattern 0 1 diagonally or antidiagonally 13
2, 4, 4, 8, 9, 8, 16, 25, 16, 16, 32, 64, 48, 25, 32, 64, 169, 144, 81, 36, 64, 128, 441, 432, 256, 120, 49, 128, 256, 1156, 1296, 841, 400, 169, 64, 256, 512, 3025, 3888, 2704, 1360, 576, 224, 81, 512, 1024, 7921, 11664, 8836, 4624, 2025, 784, 289, 100, 1024, 2048 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....2...4...8...16...32....64...128....256.....512....1024.....2048.....4096

....4...9..25...64..169...441..1156...3025....7921...20736....54289...142129

....8..16..48..144..432..1296..3888..11664...34992..104976...314928...944784

...16..25..81..256..841..2704..8836..28561...93025..301401...980100..3179089

...32..36.120..400.1360..4624.15776..53824..183744..627264..2141568..7311616

...64..49.169..576.2025..7056.24964..87616..310249.1092025..3865156.13623481

..128..64.224..784.2800.10000.36000.129600..468000.1690000..6110000.22090000

..256..81.289.1024.3721.13456.49284.179776..660969.2421136..8916196.32729841

..512.100.360.1296.4752.17424.64416.238144..884256.3283344.12220128.45481536

.1024.121.441.1600.5929.21904.81796.304704.1142761.4276624.16080100.60341824

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..1627

FORMULA

Empirical: a(n,1) = 2^n

Empirical: a(n,2) = n^2 + 2*n + 1

Empirical: a(n,3) = 2*a(n-1,3) - 2*a(n-3,3) + a(n-4,3)

Empirical: a(n,4) = 16*n^2

Empirical: a(n,5) = 2*a(n-1,5) - 2*a(n-3,5) + a(n-4,5) for n>5

Empirical: a(n,6) = 256*n^2 - 384*n + 144 for n>2

Empirical: a(n,7) = 2*a(n-1,7) - 2*a(n-3,7) + a(n-4,7) for n>7

Empirical: a(n,8) = 4096*n^2 - 11264*n + 7744 for n>4

EXAMPLE

Some solutions for 5X3

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

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

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

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

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

CROSSREFS

Column 2 is A000290(n+1)

Column 4 is A016802

Row 2 is A007598(n+2)

Sequence in context: A048656 A107848 A285273 * A181212 A233394 A029599

Adjacent sequences:  A188821 A188822 A188823 * A188825 A188826 A188827

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Apr 11 2011

STATUS

approved

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)