A270512 Number of 4X4X4 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.

126, 5406, 132474, 1522068, 12034134, 65046258, 286690914, 1009836744, 3156450798, 8543466150, 21426975306, 48675627036, 104954386374, 210632574138, 407075899314, 745193641488, 1325939440734, 2261420632494, 3772499260698

Offset

1,1

Comments

Row 4 of A270509.

Links

R. H. Hardin, Table of n, a(n) for n = 1..58

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 - 162*n^8 + 945*n^7 - 3462*n^6 + 8976*n^5 - 15984*n^4 + 19011*n^3 - 13479*n^2 + 4305*n

Empirical for n mod 2 = 1: a(n) = 18*n^9 - 162*n^8 + 972*n^7 - 3768*n^6 + 10716*n^5 - 21954*n^4 + 32355*n^3 - 32223*n^2 + 19353*n - 5181

Example

Some solutions for n=3
.....2........1........2........0........2........2........0........3
....0.1......0.0......1.1......1.0......1.0......0.1......0.3......2.0
...0.2.0....1.1.0....0.0.0....1.2.0....1.0.3....0.2.0....1.3.2....0.2.0
..3.2.1.0..2.0.1.3..0.2.2.3..3.0.0.1..0.3.3.2..0.2.0.2..2.0.0.1..2.3.0.2

Crossrefs

Cf. A270509.

Sequence in context: A186816 A292882 A140902 * A037963 A240929 A285172

Adjacent sequences: A270509 A270510 A270511 * A270513 A270514 A270515

Keyword

nonn

Author

R. H. Hardin, Mar 18 2016

Status

approved