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A250611 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction 8
11, 26, 26, 57, 64, 57, 120, 140, 140, 120, 247, 290, 297, 290, 247, 502, 586, 592, 592, 586, 502, 1013, 1172, 1153, 1126, 1153, 1172, 1013, 2036, 2336, 2236, 2092, 2092, 2236, 2336, 2036, 4083, 4654, 4353, 3890, 3691, 3890, 4353, 4654, 4083, 8178, 9278 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...11....26....57...120...247....502...1013...2036...4083...8178..16369...32752

...26....64...140...290...586...1172...2336...4654...9278..18512..36964...73850

...57...140...297...592..1153...2236...4353...8528..16809..33292..66169..131824

..120...290...592..1126..2092...3890...7320..13982..27076..53002.104560..207350

..247...586..1153..2092..3691...6526..11749..21664..40879..78610.153289..301780

..502..1172..2236..3890..6526..10928..18664..32870..59818.112052.214660..417818

.1013..2336..4353..7320.11749..18664..30113..50192..87093.157200.293281..560872

.2036..4654..8528.13982.21664..32870..50192..78814.129104.221798.398368..741758

.4083..9278.16809.27076.40879..59818..87093.129104.198651.321334.548353..982108

.8178.18512.33292.53002.78610.112052.157200.221798.321334.486784.780100.1325186

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..881

FORMULA

Empirical: T(n,k) = 2^(n-1)*((k+1)*2)^2 + a quadratic polynomial in n

Empirical for column k (k=2 recurrence also works for k=1):

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

k=2: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=36*2^(n-1) +n^2-n-10

k=3: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=64*2^(n-1) +5*n^2+4*n-16

k=4: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=100*2^(n-1) +16*n^2+22*n-18

k=5: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=144*2^(n-1) +42*n^2+69*n-8

k=6: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=196*2^(n-1) +99*n^2+177*n+30

k=7: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n)=256*2^(n-1) +219*n^2+410*n+128

Empirical for diagonal: a(n) = 11*a(n-1) -52*a(n-2) +138*a(n-3) -225*a(n-4) +231*a(n-5) -146*a(n-6) +52*a(n-7) -8*a(n-8)

EXAMPLE

Some solutions for n=6 k=4

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

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

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

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

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

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

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

CROSSREFS

Column 1 is A000295(n+3)

Sequence in context: A220434 A191720 A066956 * A137015 A260903 A316315

Adjacent sequences:  A250608 A250609 A250610 * A250612 A250613 A250614

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 26 2014

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)