A270258 Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n exactly once.

0, 66, 768, 4428, 14976, 42750, 96768, 203448, 376320, 668250, 1094400, 1746756, 2636928, 3910998, 5569536, 7830000, 10672128, 14404338, 18973440, 24800700, 31785600, 40486446, 50738688, 63264168, 77815296, 95306250, 115385088

Offset

1,2

Comments

Row 3 of A270256.

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)

Empirical for n mod 2 = 0: a(n) = 9*n^5 - 27*n^4 + 42*n^3 - 39*n^2 + 15*n

Empirical for n mod 2 = 1: a(n) = 9*n^5 - 27*n^4 + 30*n^3 + 6*n^2 - 39*n + 21

Example

Some solutions for n=4
....3......2......2......0......2......1......0......2......4......4......3
...2.2....1.4....0.3....1.0....1.3....3.0....3.2....0.3....1.3....2.3....4.4
..3.3.3..4.1.3..4.2.3..4.4.2..4.4.2..0.3.3..0.4.3..2.2.3..1.4.4..1.2.4..2.3.1

Crossrefs

Cf. A270256.

Sequence in context: A046409 A128952 A282050 * A223410 A258917 A223152

Adjacent sequences: A270255 A270256 A270257 * A270259 A270260 A270261

Keyword

nonn

Author

R. H. Hardin, Mar 14 2016

Status

approved