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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 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.)