A221577 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1.

16, 345, 4240, 26911, 117104, 395641, 1116400, 2754635, 6127696, 12553189, 24049616, 43584535, 75375280, 125247281, 201055024, 313170691, 475045520, 703848925, 1021190416, 1453929359, 2035077616, 2804800105, 3811518320

Offset

1,1

Comments

Row 7 of A221573.

Links

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

Formula

Empirical: a(n) = 1*n^7 + 3*n^6 - 7*n^5 + 29*n^4 - 41*n^3 + 45*n^2 - 33*n + 19 for n>2.

Conjectures from Colin Barker, Aug 08 2018: (Start)

G.f.: x*(16 + 217*x + 1928*x^2 + 1755*x^3 + 2336*x^4 - 1869*x^5 + 1096*x^6 - 579*x^7 + 160*x^8 - 20*x^9) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10.

(End)

Example

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

Crossrefs

Cf. A221573.

Sequence in context: A320399 A173906 A227102 * A363383 A136269 A010368

Adjacent sequences: A221574 A221575 A221576 * A221578 A221579 A221580

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved