A212031 Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element at a city block distance of two, and containing the value n(n+1)/2-2.

0, 3, 10, 31, 78, 166, 313, 540, 871, 1333, 1956, 2773, 3820, 5136, 6763, 8746, 11133, 13975, 17326, 21243, 25786, 31018, 37005, 43816, 51523, 60201, 69928, 80785, 92856, 106228, 120991, 137238, 155065, 174571, 195858, 219031, 244198, 271470, 300961

Offset

1,2

Comments

Column 1 of A212036.

Links

R. H. Hardin, Table of n, a(n) for n = 1..70

Formula

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (17/8)*n^2 + (19/4)*n - 2 for n>1.

Conjectures from Colin Barker, Jul 20 2018: (Start)

G.f.: x^2*(3 - 5*x + 11*x^2 - 7*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.

(End)

Example

Some solutions for n=4:
..0........0........0........0........0........0........0........0
..1.2......1.2......1.2......1.2......1.2......1.1......1.2......1.2
..1.3.4....3.2.4....3.4.5....3.4.5....3.0.4....2.3.4....3.4.5....3.4.1
..5.6.7.8..5.6.7.8..6.7.3.8..6.7.8.6..5.6.7.8..5.6.7.8..5.6.7.8..5.6.7.8

Crossrefs

Cf. A212036.

Sequence in context: A331780 A360563 A290061 * A339032 A374925 A033121

Adjacent sequences: A212028 A212029 A212030 * A212032 A212033 A212034

Keyword

nonn

Author

R. H. Hardin, Apr 27 2012

Status

approved