A268461 Number of length-7 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.

29, 1169, 11536, 62535, 240170, 736525, 1926444, 4474451, 9476950, 18644745, 34530920, 60809119, 102607266, 166901765, 262977220, 402956715, 602407694, 881028481, 1263420480, 1779951095, 2467712410, 3371580669, 4545381596

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + 7*n^6 + 16*n^5 + 5*n^4 - 7*n^3 + 18*n^2 - 5*n - 5 for n>1.

Conjectures from Colin Barker, Jan 14 2019: (Start)

G.f.: x*(29 + 937*x + 2996*x^2 + 1355*x^3 - 536*x^4 + 335*x^5 - 88*x^6 + 13*x^7 - x^8) / (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>9.

(End)

Example

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

Crossrefs

Row 7 of A268457.

Sequence in context: A237356 A176695 A210303 * A025761 A003735 A159479

Adjacent sequences: A268458 A268459 A268460 * A268462 A268463 A268464

Keyword

nonn

Author

R. H. Hardin, Feb 04 2016

Status

approved