A270259 Number of 4X4X4 triangular 0..n arrays with some element plus some adjacent element totalling n exactly once.

0, 468, 37848, 772056, 7876728, 51535116, 241185744, 924548976, 2925247440, 8286296580, 20750653800, 48470046408, 103934097288, 212501629116, 408044064288, 756921118176, 1338316241184, 2305178257716, 3823090748280

Offset

1,2

Comments

Row 4 of A270256.

Links

R. H. Hardin, Table of n, a(n) for n = 1..59

Formula

Empirical: a(n) = 2*a(n-1) +7*a(n-2) -16*a(n-3) -20*a(n-4) +56*a(n-5) +28*a(n-6) -112*a(n-7) -14*a(n-8) +140*a(n-9) -14*a(n-10) -112*a(n-11) +28*a(n-12) +56*a(n-13) -20*a(n-14) -16*a(n-15) +7*a(n-16) +2*a(n-17) -a(n-18)

Empirical for n mod 2 = 0: a(n) = 18*n^9 - 144*n^8 + 612*n^7 - 1746*n^6 + 3618*n^5 - 5502*n^4 + 5904*n^3 - 4002*n^2 + 1278*n

Empirical for n mod 2 = 1: a(n) = 18*n^9 - 144*n^8 + 585*n^7 - 1440*n^6 + 2178*n^5 - 1641*n^4 - 522*n^3 + 2502*n^2 - 2259*n + 723

Example

Some solutions for n=3
.....0........3........1........3........2........3........1........1
....2.2......1.2......0.0......2.0......0.0......3.3......1.1......1.0
...3.3.1....1.3.3....2.0.0....0.2.0....2.0.2....1.1.3....0.1.3....3.1.1
..3.2.3.3..1.3.2.2..2.2.2.3..0.0.0.0..0.2.3.2..0.0.0.1..0.1.0.2..1.0.1.1

Crossrefs

Cf. A270256.

Sequence in context: A205408 A282116 A281061 * A205407 A045305 A349275

Adjacent sequences: A270256 A270257 A270258 * A270260 A270261 A270262

Keyword

nonn

Author

R. H. Hardin, Mar 14 2016

Status

approved