A212826 Number of 0..5 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..5 order.

1, 2, 5, 13, 44, 168, 716, 3331, 16599, 87059, 473569, 2641428, 14982656, 85930423, 496412949, 2881216925, 16773626497, 97843056510, 571457023718, 3340356838651, 19535838889479, 114293073644447, 668811749036809, 3914263576403496

Offset

1,2

Comments

Column 5 of A212829.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8) for n>11.

Empirical g.f.: x*(1 + x + x^2)*(1 - 10*x + 22*x^2 + 27*x^3 - 68*x^4 - 67*x^5 + 29*x^6 + 44*x^7 + 11*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - Colin Barker, Jul 21 2018

Example

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....0....1....1....1....1....1....1....1....1....1....1....1
..1....2....1....2....0....1....1....2....0....1....2....2....0....1....2....1
..0....3....2....0....1....2....2....3....2....2....1....3....2....2....3....0
..2....3....3....0....0....3....3....0....1....1....0....2....2....3....4....2
..3....4....1....0....2....4....2....2....1....0....3....1....2....4....5....3
..1....3....2....1....2....2....4....3....3....0....2....0....3....3....4....2
..1....3....3....1....3....4....3....3....1....2....1....2....1....5....4....0

Crossrefs

Cf. A212829.

Sequence in context: A119533 A066740 A212825 * A212827 A212828 A212830

Adjacent sequences: A212823 A212824 A212825 * A212827 A212828 A212829

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved