A253841 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally

512, 2440, 2440, 8392, 6339, 8392, 28540, 17491, 19970, 28540, 91296, 50462, 52014, 60741, 91296, 263476, 127376, 135011, 127483, 129378, 263476, 709704, 308576, 294870, 284109, 135280, 265117, 709704, 1850176, 697720, 654021, 550535, 167413

Offset

1,1

Comments

Table starts

......512....2440...8392..28540..91296..263476..709704.1850176.4685448.11503856

.....2440....6339..17491..50462.127376..308576..697720.1437880.2829830..5401152

.....8392...19970..52014.135011.294870..654021.1364704.2573789.4642528..8066302

....28540...60741.127483.284109.550535.1139506.2282367.3961764.7017601.11724584

....91296..129378.135280.167413.156876..237202..350208..545216..885886..1475884

...263476..265117.201331.204420.209862..295098..427510..627452..963880..1514191

...709704..517697.233370.196053.168884..225776..262418..401447..624346..1006728

..1850176..920743.230890.121909..85994..103499..145955..218499..355399...604877

..4685448.1570681.276234.138562..98010..121541..159924..226306..347440...572140

.11503856.2618604.303500.139402.105807..121166..165378..232606..358554...571191

Links

R. H. Hardin, Table of n, a(n) for n = 1..909

Formula

Empirical for column k:

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

k=2: [order 26] for n>30

k=3: [order 22] for n>36

k=4: [same order 22] for n>34

k=5: [same order 22] for n>34

k=6: [same order 22] for n>35

k=7: [same order 22] for n>35

Empirical for row n:

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

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

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

n=4: [order 54] for n>86

n=5: [order 46] for n>67

n=6: [order 47] for n>71

n=7: [order 48] for n>75

Empirical quasipolynomials for column k:

k=3: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 24 for n>14

k=4: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 24 for n>12

k=5: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 24 for n>12

k=6: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 24 for n>13

k=7: polynomial of degree 4 plus a quasipolynomial of degree 2 with period 24 for n>13

Empirical quasipolynomials for row n:

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

n=4: polynomial of degree 14 plus a quasipolynomial of degree 8 with period 24 for n>32

n=5: polynomial of degree 15 plus a quasipolynomial of degree 5 with period 24 for n>21

n=6: polynomial of degree 16 plus a quasipolynomial of degree 5 with period 24 for n>24

n=7: polynomial of degree 17 plus a quasipolynomial of degree 5 with period 24 for n>27

Example

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

Crossrefs

Sequence in context: A254907 A257209 A254900 * A253935 A253834 A259006

Adjacent sequences: A253838 A253839 A253840 * A253842 A253843 A253844

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 16 2015

Status

approved