A196212 -id:A196212 - cp's OEIS frontend

A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.

1, 3, 1, 4, 9, 1, 5, 25, 20, 1, 9, 49, 77, 61, 1, 16, 149, 117, 385, 189, 1, 25, 625, 278, 572, 2099, 544, 1, 39, 2141, 1959, 3851, 4336, 9083, 1629, 1, 64, 5433, 11044, 44623, 62104, 19750, 48188, 4973, 1, 105, 17269, 36730, 347576, 1285961, 326145, 102201, 249446

Offset: 1

R. H. Hardin, Dec 21 2015

Table starts
.1.....3.......4........5.........9.........16..........25.........39
.1.....9......25.......49.......149........625........2141.......5433
.1....20......77......117.......278.......1959.......11044......36730
.1....61.....385......572......3851......44623......347576....1650710
.1...189....2099.....4336.....62104....1285961....16386099..124675418
.1...544....9083....19750....326145...13689944...325554385.3901509248
.1..1629...48188...102201...4176690..311260836.10444421518
.1..4973..249446...620508..50677045.6688962679
.1.15040.1166325..3041449.367191341
.1.45739.6288299.16217839

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

R. H. Hardin, Table of n, a(n) for n = 1..97

Column 2 is A196212.

Row 1 is A195971.

Empirical for column k:
k=1: a(n) = a(n-1),
k=2: [order 10],
k=3: [order 26] for n>27,
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3) +a(n-4),
n=2: [order 17],
n=3: [order 77].

A196685 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 20, 20, 5, 9, 61, 58, 61, 9, 16, 189, 292, 292, 189, 16, 25, 544, 1235, 2245, 1235, 544, 25, 39, 1629, 5186, 15395, 15395, 5186, 1629, 39, 64, 4973, 22461, 109528, 188078, 109528, 22461, 4973, 64, 105, 15040, 96256, 796557, 2169685

Offset: 1

R. H. Hardin Oct 05 2011

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 2's, every 4 is next to 4 3's
Table starts
...1.....3.......4.........5...........9............16..............25
...3.....9......20........61.........189...........544............1629
...4....20......58.......292........1235..........5186...........22461
...5....61.....292......2245.......15395........109528..........796557
...9...189....1235.....15395......188078.......2169685........25142624
..16...544....5186....109528.....2169685......39696088.......741925729
..25..1629...22461....796557....25142624.....741925729.....23029545105
..39..4973...96256...5702355...291420839...14189246566....718199634805
..64.15040..413032..40479328..3417608122..269528695666..22138818455076
.105.45739.1780597.289195575.40048090008.5096101360077.682005890331480

			Some solutions for n=6 k=4
..0..0..1..1....1..1..0..1....0..0..0..1....0..0..0..0....1..0..0..0
..1..1..2..0....0..1..1..1....0..0..0..2....1..1..2..0....1..2..1..1
..2..1..0..0....0..1..1..0....0..0..0..1....2..2..1..0....0..2..1..2
..0..1..2..0....0..1..1..0....1..2..1..2....1..2..2..0....1..1..0..0
..2..1..1..0....0..2..1..0....1..0..2..0....0..1..1..2....1..1..0..0
..1..0..2..1....0..0..2..1....2..1..1..0....1..2..0..1....0..1..2..1

R. H. Hardin, Table of n, a(n) for n = 1..144

Column 1 is A195971

Column 2 is A196212

cp's OEIS Frontend

A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.

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