A221541 Number of 0..7 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

0, 7, 44, 350, 2658, 20386, 156098, 1195561, 9156379, 70126074, 537074685, 4113296146, 31502516844, 241268447450, 1847803587081, 14151780448318, 108384295414048, 830083220654363, 6357361558503534, 48689149448999134

Offset

1,2

Comments

Column 7 of A221542.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8).

Empirical g.f.: x^2*(7 - 5*x + 14*x^2 - 3*x^3 + 20*x^4 - 6*x^5) / (1 - 7*x - 4*x^2 - 5*x^3 - 20*x^4 - 20*x^5 - 23*x^6 + 6*x^7 - 3*x^8). - Colin Barker, Oct 18 2017

Example

Some solutions for n=6
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..4....7....6....3....0....4....3....2....0....0....0....2....4....2....3....4
..2....5....3....2....6....1....4....7....3....4....6....6....0....5....2....1
..4....6....6....4....6....4....1....0....6....4....5....6....2....0....0....7
..4....2....7....1....7....3....7....2....3....0....5....6....2....6....4....4
..6....7....5....7....4....6....4....6....0....3....5....1....7....2....0....1

Crossrefs

Sequence in context: A093738 A091127 A166775 * A327680 A156374 A171493

Adjacent sequences: A221538 A221539 A221540 * A221542 A221543 A221544

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved