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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.)