A270853 Number of 4X4X4 triangular 0..n arrays with some element plus some adjacent element totalling n+1, n or n-1 exactly once.

0, 0, 252, 6822, 108348, 1144464, 8559378, 49511370, 225803628, 868915644, 2866094766, 8402366160, 22207133946, 53934812124, 121777854570, 258248878044, 519141258054, 994719606876, 1830153826026, 3242675095548, 5566018125510

Offset

1,3

Comments

Row 4 of A270850.

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) for n>33

Empirical for n mod 2 = 0: a(n) = 54*n^9 - 2304*n^8 + 48114*n^7 - 640560*n^6 + 5967942*n^5 - 40260606*n^4 + 196350792*n^3 - 666434964*n^2 + 1425184728*n - 1458389412 for n>15

Empirical for n mod 2 = 1: a(n) = 54*n^9 - 2304*n^8 + 48141*n^7 - 641856*n^6 + 5994894*n^5 - 40583919*n^4 + 198797448*n^3 - 678190998*n^2 + 1458498405*n - 1501345395 for n>15

Example

Some solutions for n=4
.....0........3........0........3........2........4........1........2
....1.0......4.4......0.1......4.4......3.4......0.2......2.0......0.0
...0.1.1....2.4.4....2.0.1....3.4.2....3.3.4....0.0.0....0.0.0....0.1.2
..0.2.0.1..3.4.4.4..0.1.1.1..4.3.4.3..3.4.3.3..2.0.1.0..0.0.1.0..0.0.0.0

Crossrefs

Cf. A270850.

Sequence in context: A151610 A250085 A024018 * A177301 A250376 A329755

Adjacent sequences: A270850 A270851 A270852 * A270854 A270855 A270856

Keyword

nonn

Author

R. H. Hardin, Mar 24 2016

Status

approved