A211905 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-2.

0, 2, 10, 34, 86, 181, 337, 575, 919, 1396, 2036, 2872, 3940, 5279, 6931, 8941, 11357, 14230, 17614, 21566, 26146, 31417, 37445, 44299, 52051, 60776, 70552, 81460, 93584, 107011, 121831, 138137, 156025, 175594, 196946, 220186, 245422, 272765, 302329

Offset

1,2

Comments

Column 1 of A211910.

Links

R. H. Hardin, Table of n, a(n) for n = 1..76

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (9/8)*n^2 + (3/4)*n + 1 for n>1.

Example

Some solutions for n=4:
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.2......1.2......1.2
..3.4.5....3.4.5....3.0.4....3.4.5....3.4.5....3.4.3....3.4.5....3.4.5
..6.0.7.8..6.7.8.7..5.6.7.8..6.7.4.8..6.7.8.4..5.6.7.8..6.1.7.8..6.7.0.8

Crossrefs

Sequence in context: A108100 A059924 A304159 * A022498 A036799 A190161

Adjacent sequences: A211902 A211903 A211904 * A211906 A211907 A211908

Keyword

nonn

Author

R. H. Hardin, Apr 25 2012

Status

approved