A250364 Number of length 6 arrays x(i), i=1..6 with x(i) in i..i+n and no value appearing more than 3 times.

64, 729, 4048, 15365, 45866, 115963, 259106, 526505, 992530, 1760831, 2971178, 4807021, 7503770, 11357795, 16736146, 24086993, 33950786, 46972135, 63912410, 85663061, 113259658, 147896651, 190942850, 243957625, 308707826, 387185423

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 5*n^3 + 57*n^2 + 13*n + 1 for n>3.

Conjectures from Colin Barker, Nov 13 2018: (Start)

G.f.: x*(64 + 281*x + 289*x^2 + 98*x^3 + 44*x^4 + 57*x^5 - 405*x^6 + 482*x^7 - 232*x^8 + 42*x^9) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.

(End)

Example

Some solutions for n=6:
..2....1....5....4....5....4....1....0....0....1....5....4....5....5....0....4
..2....6....4....7....2....6....4....1....1....5....5....4....1....3....4....4
..3....8....6....7....2....7....6....3....7....4....8....8....6....2....7....7
..8....7....4....5....7....7....8....5....5....4....8....8....8....9....9....7
..8....7....4....5....4....7....4....9....8....8....4....9....6....8....4....8
..7...11....7...10....7....8....8....6....5....6...10....7....9....6....7....8

Crossrefs

Row 6 of A250361.

Sequence in context: A223953 A224137 A016899 * A346638 A017676 A055015

Adjacent sequences: A250361 A250362 A250363 * A250365 A250366 A250367

Keyword

nonn

Author

R. H. Hardin, Nov 19 2014

Status

approved