A246482 Number of length 3+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

2, 20, 292, 1376, 6534, 20004, 57416, 133664, 293770, 574100, 1073772, 1865280, 3134222, 5007716, 7797904, 11708864, 17227026, 24659604, 34722740, 47856800, 65070742, 86971940, 114932952, 149765856, 193285274, 246549524, 311901436

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).

Conjectures from Colin Barker, Nov 06 2018: (Start)

G.f.: 2*x*(1 + 7*x + 115*x^2 + 251*x^3 + 1161*x^4 + 1045*x^5 + 2001*x^6 + 617*x^7 + 562*x^8) / ((1 - x)^7*(1 + x)^4).

a(n) = -20*n + 43*n^2 - 40*n^3 + 21*n^4 - 6*n^5 + n^6 for n even.

a(n) = -26 + 37*n + 5*n^2 - 30*n^3 + 21*n^4 - 6*n^5 + n^6 for n odd.

(End)

Example

Some solutions for n=6:
..3....6....2....5....5....3....1....6....6....4....2....6....1....1....1....5
..4....4....2....3....5....5....0....1....4....4....1....2....2....2....6....2
..1....5....2....5....3....5....3....3....6....4....6....5....0....6....2....6
..0....3....2....6....2....6....4....1....3....4....6....2....3....2....3....5
..3....0....2....6....2....4....0....2....4....4....6....6....2....1....5....5
..2....5....6....5....1....3....0....2....6....1....3....6....1....3....0....6

Crossrefs

Row 3 of A246479.

Sequence in context: A326010 A363380 A349963 * A124211 A277308 A128481

Adjacent sequences: A246479 A246480 A246481 * A246483 A246484 A246485

Keyword

nonn

Author

R. H. Hardin, Aug 27 2014

Status

approved