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A195248 T(n,k) = Number of lower triangles of an n X n 0..k array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by two or less. 11
2, 3, 8, 4, 27, 64, 5, 46, 729, 1024, 6, 65, 1682, 59049, 32768, 7, 84, 2729, 190514, 14348907, 2097152, 8, 103, 3776, 357847, 67379894, 10460353203, 268435456, 9, 122, 4823, 533142, 147824001, 74236765958, 22876792454961, 68719476736, 10, 141 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.......2...........3...........4............5............6............7

.......8..........27..........46...........65...........84..........103

......64.........729........1682.........2729.........3776.........4823

....1024.......59049......190514.......357847.......533142.......709613

...32768....14348907....67379894....147824001....237368212....329060365

.2097152.10460353203.74236765958.192172956591.333437946202.481573562101

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..132

FORMULA

Empirical for rows:

T(1,k) = 1*k + 1,

T(2,k) = 19*k - 11

T(3,k) = 1047*k - 1459 for k>2,

T(4,k) = 176471*k - 349213 for k>4,

T(5,k) = 92031109*k - 223153377 for k>6,

T(6,k) = 149824887097*k - 417651128341 for k>8,

T(7,k) = 764465228592699*k - 2364216638005277 for k>10,

Generalizing, T(n,k) = A195214(n)*k + const(n) for k>2*n-4.

EXAMPLE

Some solutions for n=6, k=5

..4............1............5............0............0............1

..5.3..........1.3..........5.4..........1.2..........0.2..........0.0

..5.4.5........1.2.4........3.4.4........1.3.1........1.0.0........2.1.2

..4.3.4.4......3.3.3.3......5.3.5.4......2.1.1.2......0.1.1.0......0.0.2.2

..5.4.2.2.4....4.5.4.5.5....4.3.5.4.3....2.3.1.3.1....2.0.2.2.0....2.0.1.2.4

..4.3.2.2.4.4..3.5.3.3.5.5..3.5.5.3.3.1..4.2.2.1.1.0..0.2.0.2.0.1..1.1.0.2.4.4

CROSSREFS

Column 1 is A006125(n+1).

Column 2 is A047656(n+1).

Cf. A195214.

Sequence in context: A195232 A093898 A194931 * A229870 A202651 A334859

Adjacent sequences:  A195245 A195246 A195247 * A195249 A195250 A195251

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 13 2011

STATUS

approved

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Last modified August 7 15:42 EDT 2022. Contains 355994 sequences. (Running on oeis4.)