A221518 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 8, 248, 2088, 9940, 33860, 92934, 219352, 463208, 898020, 1626970, 2789864, 4570812, 7206628, 10995950, 16309080, 23598544, 33410372, 46396098, 63325480, 85099940, 112766724, 147533782, 190785368, 244098360, 309259300, 388282154

Offset

1,2

Comments

Row 7 of A221515.

Links

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

Formula

Empirical: a(n) = 1*n^6 + 1*n^5 - 29*n^4 + 104*n^3 - 173*n^2 + 136*n - 40 for n>3.

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

G.f.: 2*x^2*(4 + 96*x + 260*x^2 + 126*x^3 - 136*x^4 + 43*x^5 - 49*x^6 + 19*x^7 - 3*x^8) / (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:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..6....5....3....5....5....4....3....5....6....6....3....6....6....6....3....5
..0....1....0....1....0....6....5....5....2....5....6....1....2....0....0....6
..5....1....2....4....2....6....2....1....4....2....6....0....1....2....5....0
..2....5....4....0....4....0....6....5....2....6....0....6....5....5....1....0
..6....6....5....2....5....0....2....2....4....3....3....5....5....0....6....4
..0....4....2....6....0....2....4....0....1....5....1....3....2....5....3....6

Crossrefs

Cf. A221515.

Sequence in context: A219269 A029751 A035036 * A317519 A300202 A347107

Adjacent sequences: A221515 A221516 A221517 * A221519 A221520 A221521

Keyword

nonn

Author

R. H. Hardin, Jan 18 2013

Status

approved