A209469 Number of n X 1 0..2 arrays with every element value z a city block distance of exactly z from another element value z.

1, 2, 5, 10, 21, 46, 97, 207, 437, 920, 1941, 4090, 8630, 18217, 38456, 81197, 171420, 361878, 763917, 1612552, 3403944, 7185413, 15167839, 32018305, 67588649, 142675574, 301179445, 635771007, 1342072303, 2833028679, 5980341655

Offset

1,2

Comments

Column 1 of A209476.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + 4*a(n-5) - 3*a(n-6) + 3*a(n-7) + a(n-8) - 2*a(n-9) + a(n-10) - a(n-11).

Empirical g.f.: x*(1 + x + x^2)*(1 - 2*x + 2*x^2 - x^3 + x^4 + x^5 - x^6 + x^7 - x^8) / (1 - 3*x + 2*x^2 + x^4 - 4*x^5 + 3*x^6 - 3*x^7 - x^8 + 2*x^9 - x^10 + x^11). - Colin Barker, Jul 10 2018

Example

Some solutions for n=8:
..0....0....1....0....0....0....2....1....0....2....0....1....0....0....2....0
..0....2....1....1....0....0....2....1....0....2....1....1....0....0....0....1
..0....0....1....1....0....1....2....0....1....2....1....0....2....0....2....1
..1....2....1....1....0....1....2....2....1....2....2....0....2....1....0....0
..1....0....0....1....0....0....2....0....1....0....0....0....2....1....0....0
..0....1....0....0....0....1....1....2....0....1....2....0....2....2....1....0
..1....1....1....1....0....1....1....0....1....1....1....0....1....0....1....0
..1....0....1....1....0....1....0....2....1....1....1....0....1....2....0....0

Crossrefs

Cf. A209476.

Sequence in context: A052540 A018106 A247594 * A208275 A327764 A192317

Adjacent sequences: A209466 A209467 A209468 * A209470 A209471 A209472

Keyword

nonn

Author

R. H. Hardin, Mar 09 2012

Status

approved