A268321 Number of length-(n+1) 0..2 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

2, 4, 10, 25, 66, 177, 485, 1348, 3797, 10812, 31076, 90015, 262432, 769199, 2264475, 6690450, 19825011, 58884842, 175238730, 522316253, 1558776782, 4656673837, 13922711281, 41654206400, 124688153137, 373402997944, 1118614401040

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 21*a(n-4) - 7*a(n-5) - 6*a(n-6).

Empirical g.f.: x*(2 - 10*x + 10*x^2 + 11*x^3 - 11*x^4 - 5*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)). - Colin Barker, Jan 13 2019

Example

Some solutions for n=10:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....0....1....0....1....0....0....0....0....0....1....1....1
..1....0....0....1....0....0....1....2....1....1....1....1....1....0....0....2
..2....0....2....1....1....2....1....0....2....1....1....0....2....2....1....1
..1....0....0....2....1....0....1....0....1....0....0....1....0....0....2....0
..2....1....0....1....1....1....1....0....1....2....1....1....2....0....0....1
..1....1....2....1....1....2....1....1....2....2....0....1....1....2....1....0
..1....0....0....0....1....0....0....2....0....0....0....2....2....1....2....0
..2....1....0....2....2....2....0....0....0....2....1....2....0....1....1....0
..1....2....2....1....0....0....2....1....1....0....2....1....0....2....2....2
..1....1....1....1....0....2....2....0....1....1....0....2....1....0....1....0

Crossrefs

Column 2 of A268327.

Sequence in context: A230552 A230555 A189912 * A195981 A124500 A220872

Adjacent sequences: A268318 A268319 A268320 * A268322 A268323 A268324

Keyword

nonn

Author

R. H. Hardin, Feb 01 2016

Status

approved