A270511 Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.

15, 144, 1137, 4584, 15843, 40392, 95109, 189936, 362487, 625440, 1048665, 1643544, 2526027, 3699864, 5343213, 7443552, 10259679, 13751856, 18280257, 23764680, 30689715, 38919144, 49087317, 60984144, 75421383, 92094912, 112023849

Offset

1,1

Comments

Row 3 of A270509.

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 - 36*n^4 + 96*n^3 - 111*n^2 + 54*n

Empirical for n mod 2 = 1: a(n) = 9*n^5 - 36*n^4 + 108*n^3 - 156*n^2 + 132*n - 42

Example

Some solutions for n=4
....4......1......3......2......1......0......3......1......2......0......3
...3.2....4.0....3.3....4.1....3.3....3.1....4.1....3.0....2.1....2.0....3.4
..3.0.1..3.3.4..0.1.4..3.3.0..2.0.3..4.1.3..4.0.1..0.2.0..4.4.2..0.3.3..3.1.3

Crossrefs

Cf. A270509.

Sequence in context: A240158 A255944 A243418 * A026893 A368075 A163799

Adjacent sequences: A270508 A270509 A270510 * A270512 A270513 A270514

Keyword

nonn

Author

R. H. Hardin, Mar 18 2016

Status

approved