A254568 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the four sums of the central row, central column, diagonal and antidiagonal nondecreasing horizontally and vertically

512, 2384, 2384, 10240, 10870, 10240, 37200, 54212, 54212, 37200, 116056, 183210, 312322, 183210, 116056, 358324, 536906, 978154, 978154, 536906, 358324, 1029664, 1612832, 2647806, 2148260, 2647806, 1612832, 1029664, 2800912, 4205934, 7796356

Offset

1,1

Comments

Table starts

......512.....2384.....10240.....37200....116056.....358324....1029664

.....2384....10870.....54212....183210....536906....1612832....4205934

....10240....54212....312322....978154...2647806....7796356...20277514

....37200...183210....978154...2148260...4796417...12136355...25618602

...116056...536906...2647806...4796417..10679860...25591173...45085796

...358324..1612832...7796356..12136355..25591173...67038844..120967261

..1029664..4205934..20277514..25618602..45085796..120967261..206491388

..2800912.10525070..50757141..56219231.101378800..285405350..496247824

..7536024.25843648.124775368.118029035.196258426..585731513..980309768

.19539824.60108505.293581128.245830679.401333712.1260737905.2140733638

Links

R. H. Hardin, Table of n, a(n) for n = 1..1740

Formula

Empirical for column k:

k=1: [linear recurrence of order 48] for n>50

k=2: [order 48] for n>56

k=3: [order 51] for n>61

k=4: [order 50] for n>62

k=5: [order 49] for n>63

k=6: [order 54] for n>70

k=7: [order 53] for n>71

Empirical quasipolynomials for column k:

k=2: polynomial of degree 20 plus a quasipolynomial of degree 12 with period 6 for n>8

k=3: polynomial of degree 21 plus a quasipolynomial of degree 13 with period 6 for n>10

k=4: polynomial of degree 22 plus a quasipolynomial of degree 12 with period 6 for n>12

k=5: polynomial of degree 23 plus a quasipolynomial of degree 11 with period 6 for n>14

k=6: polynomial of degree 24 plus a quasipolynomial of degree 13 with period 6 for n>16

k=7: polynomial of degree 25 plus a quasipolynomial of degree 12 with period 6 for n>18

Example

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

Crossrefs

Sequence in context: A135273 A258522 A258519 * A254561 A254907 A257209

Adjacent sequences: A254565 A254566 A254567 * A254569 A254570 A254571

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 01 2015

Status

approved