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A195278 T(n,k) = Number of lower triangles of an n X n integer array with each element differing from all of its vertical and horizontal neighbors by k or less and triangles differing by a constant counted only once. 12
1, 1, 9, 1, 25, 171, 1, 49, 2125, 6939, 1, 81, 11319, 626525, 609309, 1, 121, 39609, 12608631, 649112125, 116330103, 1, 169, 107811, 119743353, 68604760497, 2375645170875, 48439766655, 1, 225, 248261, 724789395, 2266745635377 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

.........1.............1................1..................1

.........9............25...............49.................81

.......171..........2125............11319..............39609

......6939........626525.........12608631..........119743353

....609309.....649112125......68604760497......2266745635377

.116330103.2375645170875.1833160598134397.270149651796118149

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..74

FORMULA

Empirical for rows:

T(1,k) = 1;

T(2,k) = 4*k^2 + 4*k + 1;

T(3,k) = (64/3)*k^5 + (160/3)*k^4 + 56*k^3 + (92/3)*k^2 + (26/3)*k + 1;

T(4,k) = (49024/315)*k^9 + (24512/35)*k^8 + (457792/315)*k^7 + (81824/45)*k^6 + (67912/45)*k^5 + (38756/45)*k^4 + (11832/35)*k^3 + (27752/315)*k^2 + (1454/105)*k + 1;

T(5,k) = (735698944/467775)*k^14 + (735698944/66825)*k^13 + (5736600832/155925)*k^12 + (36310211072/467775)*k^11 + (4906182016/42525)*k^10 + (603389056/4725)*k^9 + (4615314688/42525)*k^8 + (3060288256/42525)*k^7 + (176877304/4725)*k^6 + (647154728/42525)*k^5 + (2229757561/467775)*k^4 + (174277454/155925)*k^3 + (1380143/7425)*k^2 + (68144/3465)*k + 1;

EXAMPLE

Some solutions for n=6, k=5

...0..................0..................0..................0

...3..0...............0.-4..............-4.-4...............2.-2

...4..5.10...........-3..1.-4...........-3.-3..0............3..0.-2

...7..5..7..4........-1.-3.-4.-8.........2..0..1.-3.........7..5..1..1

...2..2..3..0..5.....-5..0.-5.-6.-9......6..2..3.-2..3......3..6..4..2.-3

..-2..1..0..1..1.-1..-2..0.-4.-6-10.-5..11..6..1.-4.-1..4...1..4..3..0.-5.-8

CROSSREFS

Sequence in context: A191871 A181318 A202006 * A092477 A019433 A276634

Adjacent sequences:  A195275 A195276 A195277 * A195279 A195280 A195281

KEYWORD

nonn,tabl,changed

AUTHOR

R. H. Hardin, Sep 14 2011

STATUS

approved

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Last modified June 28 11:37 EDT 2022. Contains 354905 sequences. (Running on oeis4.)