A253935 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally and vertically

512, 2440, 2440, 8392, 8384, 8392, 28540, 30184, 30184, 28540, 91296, 109666, 124496, 109666, 91296, 263476, 299727, 451721, 451721, 299727, 263476, 709704, 756553, 992616, 1664470, 992616, 756553, 709704, 1850176, 1786831, 2326216

Offset

1,1

Comments

Table starts

......512.....2440.....8392....28540....91296...263476....709704...1850176

.....2440.....8384....30184...109666...299727...756553...1786831...3803056

.....8392....30184...124496...451721...992616..2326216...4928792...8796936

....28540...109666...451721..1664470..3152822..6795110..13179071..20815359

....91296...299727...992616..3152822..3515548..6348659...9470400..11628396

...263476...756553..2326216..6795110..6348659.11962178..17762028..22189517

...709704..1786831..4928792.13179071..9470400.17762028..31663440..40874791

..1850176..3803056..8796936.20815359.11628396.22189517..40874791..59454484

..4685448..7637333.15429736.34379873.17673400.34970988..67588814.103307903

.11503856.14786984.25901691.54238467.27050795.55170420.114752167.184797814

Links

R. H. Hardin, Table of n, a(n) for n = 1..1102

Formula

Empirical for column k:

k=1: [linear recurrence of order 32] for n>33

k=2: [order 46] for n>58

k=3: [order 53] for n>83

k=4: [order 54] for n>90

k=5: [order 46] for n>71

k=6: [order 47] for n>77

k=7: [order 54] for n>87

Empirical quasipolynomials for column k:

k=3: polynomial of degree 13 plus a quasipolynomial of degree 8 with period 24 for n>30

k=4: polynomial of degree 14 plus a quasipolynomial of degree 8 with period 24 for n>36

k=5: polynomial of degree 15 plus a quasipolynomial of degree 5 with period 24 for n>25

k=6: polynomial of degree 17 plus a quasipolynomial of degree 7 with period 24 for n>33

k=7: polynomial of degree 17 plus a quasipolynomial of degree 7 with period 24 for n>33

Example

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

Crossrefs

Column 1 is A253834

Sequence in context: A257209 A254900 A253841 * A253834 A259006 A256904

Adjacent sequences: A253932 A253933 A253934 * A253936 A253937 A253938

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 19 2015

Status

approved