A258522 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two sums of the diagonal and antidiagonal minus the two sums of the central column and central row nondecreasing horizontally and vertically

512, 2371, 2371, 6516, 7334, 6516, 16196, 13616, 13616, 16196, 47704, 23785, 19920, 23785, 47704, 156873, 45771, 25076, 25076, 45771, 156873, 488240, 91023, 25532, 18282, 25532, 91023, 488240, 1356489, 169230, 23907, 9784, 9784, 23907, 169230

Offset

1,1

Comments

Table starts

......512....2371..6516.16196.47704.156873.488240.1356489.3595084.9838222

.....2371....7334.13616.23785.45771..91023.169230..300889..536665..960950

.....6516...13616.19920.25076.25532..23907..23398...26321...30168...33303

....16196...23785.25076.18282..9784...5331...3904....3384....2918....2518

....47704...45771.25532..9784..4028...2176...1362.....994....1054.....915

...156873...91023.23907..5331..2176...1256....767.....588.....649.....530

...488240..169230.23398..3904..1362....767....520.....442.....396.....388

..1356489..300889.26321..3384...994....588....442.....424.....348.....336

..3595084..536665.30168..2918..1054....649....396.....348.....312.....310

..9838222..960950.33303..2518...915....530....388.....336.....310.....252

.27777116.1692043.35726..2590...948....541....354.....300.....306.....246

.77335445.2898384.37801..2760...954....519....332.....282.....268.....228

Links

R. H. Hardin, Table of n, a(n) for n = 1..7562

Formula

Empirical for column k:

k=1: [linear recurrence of order 30] for n>34

k=2: [order 94] for n>105

k=3: [order 19] for n>39

k=4: a(n) = -a(n-1) -a(n-2) -a(n-3) +a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>19

k=5: a(n) = -a(n-1) -a(n-2) -a(n-3) +a(n-5) +a(n-6) +a(n-7) +a(n-8) for n>19

k=6: a(n) = a(n-5) for n>16

k=7: a(n) = -a(n-2) +a(n-5) +a(n-7) for n>18

Empirical periods for column k:

k=4: period 20 starting at n=12: 2760 2878 2779 2550 2508 2654 2902 2899 2512 2402 2678 3022 2861 2406 2426 2798 2984 2755 2430 2546

k=5: period 20 starting at n=12: 954 844 1017 896 934 918 869 1028 896 898 943 880 1028 860 923 954 880 992 885 934

k=6: period 5 starting at n=12: 519 486 567 482 521

k=7: period 20 starting at n=12: 332 348 316 340 336 336 344 312 344 340 332 340 316 348 336 328 344 320 344 332

Example

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

Crossrefs

Sequence in context: A251187 A223333 A135273 * A258519 A254568 A254561

Adjacent sequences: A258519 A258520 A258521 * A258523 A258524 A258525

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 01 2015

Status

approved