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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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 14 2011
STATUS
approved

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Last modified May 27 20:38 EDT 2024. Contains 372882 sequences. (Running on oeis4.)