A221540 Number of 0..6 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

0, 6, 32, 222, 1455, 9665, 64047, 424593, 2814515, 18656979, 123673887, 819813575, 5434406883, 36023773275, 238795558499, 1582935756291, 10493015970771, 69556445196155, 461078023878243, 3056408985571563, 20260423189286435

Offset

1,2

Comments

Column 6 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) +6*a(n-3) +26*a(n-4) +10*a(n-5) +16*a(n-6) +12*a(n-8).

Empirical g.f.: x^2*(6 - 10*x + 22*x^2 - 7*x^3 + 20*x^4 - 12*x^5 + 6*x^6) / (1 - 7*x + 4*x^2 - 6*x^3 - 26*x^4 - 10*x^5 - 16*x^6 - 12*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
..6....5....2....4....5....2....0....0....5....6....3....0....2....0....5....4
..2....2....6....1....2....1....0....6....6....6....5....6....0....4....1....0
..5....2....0....6....2....1....2....2....6....3....1....3....3....3....0....6
..5....6....0....5....6....5....6....0....6....4....5....5....4....1....3....6
..2....6....0....3....0....0....4....4....0....1....3....1....0....6....3....4

Crossrefs

Sequence in context: A146557 A020013 A283326 * A331878 A121120 A183681

Adjacent sequences: A221537 A221538 A221539 * A221541 A221542 A221543

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved