A211911 - OEIS

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A211911

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, vertical, diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.

0, 1, 6, 25, 70, 156, 301, 526, 855, 1315, 1936, 2751, 3796, 5110, 6735, 8716, 11101, 13941, 17290, 21205, 25746, 30976, 36961, 43770, 51475, 60151, 69876, 80731, 92800, 106170, 120931, 137176, 155001, 174505, 195790, 218961, 244126, 271396, 300885

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Column 1 of A211916.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..74

FORMULA

Empirical: a(n) = (1/8)*n^4 + (1/4)*n^3 - (17/8)*n^2 + (11/4)*n for n>1.

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

G.f.: x^2*(1 + x + 5*x^2 - 5*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......1.2......1.2......1.2

..3.4.5....3.4.5....3.4.5....3.4.5....3.4.5....3.4.5....3.4.1....3.4.5

..0.6.7.8..6.7.8.1..1.6.7.8..6.7.3.8..6.7.8.7..6.1.7.8..5.6.7.8..6.7.8.3

CROSSREFS

Cf. A211916.

Sequence in context: A241170 A245679 A354392 * A339194 A241303 A278473

Adjacent sequences: A211908 A211909 A211910 * A211912 A211913 A211914

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 25 2012

STATUS

approved