A212840 Number of 0..n arrays of length 7 with 0 never adjacent to n.

2, 577, 8042, 49835, 204994, 654797, 1758602, 4159927, 8927810, 17738489, 33102442, 58641827, 99423362, 162351685, 256628234, 394280687, 590768002, 865666097, 1243439210, 1754301979, 2435177282, 3330754877, 4494655882

Offset

1,1

Comments

Row 6 of A212835.

Links

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

Formula

Empirical: a(n) = n^7 + 7*n^6 + 9*n^5 - 15*n^4 - 13*n^3 + 15*n^2 - 1*n - 1.

Conjectures from Colin Barker, Jul 21 2018: (Start)

G.f.: x*(2 + 561*x + 3482*x^2 + 1543*x^3 - 682*x^4 + 151*x^5 - 18*x^6 + x^7) / (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>8.

(End)

Example

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

Crossrefs

Cf. A212835.

Sequence in context: A003830 A134371 A306635 * A129697 A214911 A203770

Adjacent sequences: A212837 A212838 A212839 * A212841 A212842 A212843

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved