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A195278
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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.
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12
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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
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..74
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FORMULA
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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;
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EXAMPLE
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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
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CROSSREFS
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Sequence in context: A191871 A181318 A202006 * A092477 A019433 A276634
Adjacent sequences: A195275 A195276 A195277 * A195279 A195280 A195281
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KEYWORD
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nonn,tabl,changed
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AUTHOR
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R. H. Hardin, Sep 14 2011
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STATUS
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approved
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