A270608 Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n+1 or n-1 exactly once.

0, 0, 312, 1716, 8148, 23448, 67788, 144252, 315936, 568032, 1049532, 1692228, 2793240, 4176936, 6369012, 9014028, 12965136, 17596272, 24205356, 31786452, 42217992, 53986488, 69705060, 87206556, 110011392, 135134208, 167193756

Offset

1,3

Comments

Row 3 of A270606.

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) for n>17

Empirical for n mod 2 = 0: a(n) = 18*n^5 - 216*n^4 + 1296*n^3 - 4464*n^2 + 8562*n - 7188 for n>7

Empirical for n mod 2 = 1: a(n) = 18*n^5 - 216*n^4 + 1392*n^3 - 5532*n^2 + 13068*n - 14058 for n>7

Example

Some solutions for n=4
....3......4......1......3......1......1......4......3......3......4......3
...4.3....4.0....1.0....3.4....3.3....2.0....2.3....3.3....2.4....4.4....4.0
..0.3.1..3.3.1..0.1.3..3.1.3..0.1.3..4.2.0..2.4.3..2.4.3..0.2.4..2.3.3..0.0.0

Crossrefs

Cf. A270606.

Sequence in context: A043360 A339074 A237551 * A233939 A233934 A289793

Adjacent sequences: A270605 A270606 A270607 * A270609 A270610 A270611

Keyword

nonn

Author

R. H. Hardin, Mar 20 2016

Status

approved