A209603 Number of n X 1 1..2 arrays with every element value z a city block distance of exactly z from another element value z.

0, 1, 1, 2, 2, 4, 6, 9, 13, 19, 27, 39, 57, 84, 124, 183, 269, 394, 576, 842, 1232, 1805, 2647, 3883, 5695, 8349, 12235, 17926, 26264, 38485, 56401, 82666, 121166, 177592, 260282, 381457, 559033, 819275, 1200683, 1759683, 2578965, 3779704, 5539476

Offset

1,4

Comments

Column 1 of A209610.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-6).

Empirical g.f.: x*(1 - x + x^2 - x^3 + 2*x^4) / ((1 - x + x^3)*(1 - x - x^3)). - Colin Barker, Jul 11 2018

Example

All solutions for n=9:
..2....2....1....1....1....2....1....1....1....2....2....1....1
..2....2....1....1....1....2....1....1....1....2....2....1....1
..2....2....2....1....1....2....1....2....1....2....2....1....2
..2....2....2....1....2....2....2....2....1....2....2....1....2
..1....2....2....1....2....2....2....2....1....2....2....2....2
..1....2....2....2....2....2....2....2....1....2....1....2....2
..1....1....2....2....2....2....2....2....1....2....1....2....1
..1....1....1....2....2....1....1....2....1....2....1....2....1
..1....1....1....2....2....1....1....2....1....2....1....2....1

Crossrefs

Cf. A209610.

Sequence in context: A237755 A362260 A306730 * A192684 A274147 A226496

Adjacent sequences: A209600 A209601 A209602 * A209604 A209605 A209606

Keyword

nonn

Author

R. H. Hardin, Mar 10 2012

Status

approved