A209469 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.