A251055 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements

66, 290, 290, 854, 1528, 854, 2243, 4334, 4334, 2243, 5449, 11280, 10289, 11280, 5449, 12858, 25847, 24893, 24893, 25847, 12858, 29759, 56676, 53306, 59215, 53306, 56676, 29759, 68506, 118925, 114512, 123396, 123396, 114512, 118925, 68506, 157205

Offset

1,1

Comments

Table starts

.....66.....290.....854....2243....5449....12858....29759....68506....157205

....290....1528....4334...11280...25847....56676...118925...247753....515324

....854....4334...10289...24893...53306...114512...237143...498593...1050871

...2243...11280...24893...59215..123396...262200...533327..1107413...2297926

...5449...25847...53306..123396..248803...521785..1045337..2159272...4456235

..12858...56676..114512..262200..521785..1081183..2129846..4324677...8753870

..29759..118925..237143..533327.1045337..2129846..4118693..8207451..16293926

..68506..247753..498593.1107413.2159272..4324677..8207451.15940227..30777666

.157205..515324.1050871.2297926.4456235..8753870.16293926.30777666..57664667

.360885.1087674.2263156.4888898.9472092.18288333.33460774.61424247.111385877

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -18*a(n-2) +17*a(n-3) +10*a(n-4) -39*a(n-5) +38*a(n-6) -17*a(n-7) +3*a(n-8) for n>9

k=2: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>11

k=3: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>12

k=4: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>12

k=5: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>12

k=6: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>12

k=7: a(n) = 8*a(n-1) -25*a(n-2) +35*a(n-3) -7*a(n-4) -49*a(n-5) +77*a(n-6) -55*a(n-7) +20*a(n-8) -3*a(n-9) for n>12

Example

Some solutions for n=4 k=4
..1..1..1..1..3....0..0..1..1..3....1..0..1..3..3....0..0..2..0..3
..0..0..0..0..2....0..0..0..0..2....1..0..0..0..0....0..0..2..0..3
..0..0..0..0..1....1..0..0..0..2....1..0..0..0..0....1..0..2..0..3
..0..0..0..0..1....1..0..0..0..2....1..0..0..0..0....1..0..2..0..3
..2..1..1..0..0....1..0..0..0..1....3..2..1..1..0....3..0..2..0..2

Crossrefs

Sequence in context: A158070 A242726 A271739 * A251048 A259292 A258958

Adjacent sequences: A251052 A251053 A251054 * A251056 A251057 A251058

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2014

Status

approved