A209367 Number of n X 1 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.

3, 8, 19, 35, 64, 110, 185, 322, 599, 1084, 1902, 3280, 5816, 10425, 18711, 33023, 58229, 102865, 183340, 326023, 578770, 1023268, 1814036, 3218397, 5719285, 10142300, 17984603, 31872737, 56560901, 100345791, 178058874, 315719677

Offset

1,1

Comments

Column 1 of A209374.

Links

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

Formula

Empirical: a(n) = a(n-2) + 4*a(n-4) + 4*a(n-5) + 5*a(n-6) - a(n-7) - 5*a(n-8) - 5*a(n-9) - 5*a(n-10) + a(n-11) + 2*a(n-12) for n>14.

Empirical g.f.: x*(3 + 8*x + 16*x^2 + 27*x^3 + 33*x^4 + 31*x^5 - 2*x^6 - 41*x^7 - 54*x^8 - 35*x^9 - 12*x^10 - 11*x^11 - 9*x^12 - 2*x^13) / ((1 - x)*(1 + x - 4*x^4 - 8*x^5 - 13*x^6 - 12*x^7 - 7*x^8 - 2*x^9 + 3*x^10 + 2*x^11)). - Colin Barker, Jul 09 2018

Example

All solutions for n=5:
..2....1....2....3....3....2....3....3....3....2....1....2....3....3
..3....3....1....3....2....1....1....1....2....3....2....3....1....3
..1....1....3....1....3....3....2....2....2....3....2....1....2....1
..2....2....3....2....1....3....2....1....1....2....3....2....2....2
..1....1....2....2....3....1....1....3....3....2....3....2....3....1

Crossrefs

Cf. A209374.

Sequence in context: A184444 A139020 A147358 * A086167 A083186 A055341

Adjacent sequences: A209364 A209365 A209366 * A209368 A209369 A209370

Keyword

nonn

Author

R. H. Hardin, Mar 07 2012

Status

approved