A270852 Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n+1, n or n-1 exactly once.

0, 0, 30, 270, 1650, 7344, 24954, 68838, 164454, 347916, 677130, 1219626, 2083038, 3373728, 5268642, 7918158, 11590422, 16482708, 22978554, 31322706, 42040590, 55422696, 72165138, 92600118, 117625542, 147608988, 183683562, 226243578

Offset

1,3

Comments

Row 3 of A270850.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -8*a(n-3) -2*a(n-4) +12*a(n-5) -2*a(n-6) -8*a(n-7) +3*a(n-8) +2*a(n-9) -a(n-10) for n>17

Empirical for n mod 2 = 0: a(n) = 27*n^5 - 531*n^4 + 4794*n^3 - 24417*n^2 + 69189*n - 86274 for n>7

Empirical for n mod 2 = 1: a(n) = 27*n^5 - 531*n^4 + 4806*n^3 - 24624*n^2 + 70425*n - 88833 for n>7

Example

Some solutions for n=4
....4......0......4......4......2......2......1......2......0......2......2
...3.4....0.1....4.4....4.4....0.0....1.0....1.0....2.0....2.2....1.0....4.4
..2.4.3..0.2.0..3.2.4..2.2.4..0.2.1..1.0.0..2.0.0..0.0.2..0.0.0..1.1.0..4.3.2

Crossrefs

Cf. A270850.

Sequence in context: A163667 A214944 A259455 * A229427 A113754 A129029

Adjacent sequences: A270849 A270850 A270851 * A270853 A270854 A270855

Keyword

nonn

Author

R. H. Hardin, Mar 24 2016

Status

approved