A212839 Number of 0..n arrays of length 6 with 0 never adjacent to n.

2, 239, 2258, 10727, 35954, 97127, 226274, 472943, 909602, 1637759, 2794802, 4561559, 7170578, 10915127, 16158914, 23346527, 33014594, 45803663, 62470802, 83902919, 111130802, 145343879, 187905698, 240370127, 304498274, 382276127

Offset

1,1

Comments

Row 5 of A212835.

Links

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

Formula

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 - 12*n^3 - 3*n^2 + 6*n - 1.

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

G.f.: x*(2 + 225*x + 627*x^2 - 130*x^3 - 12*x^4 + 9*x^5 - x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Cf. A212835.

Sequence in context: A159280 A013477 A013473 * A225784 A087226 A217972

Adjacent sequences: A212836 A212837 A212838 * A212840 A212841 A212842

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved