A250383 Number of length n+3 0..4 arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.

420, 1560, 5848, 21950, 82398, 309452, 1162292, 4365720, 16398414, 61595866, 231368150, 869073568, 3264448894, 12262057782, 46059259710, 173009763590, 649866719912, 2441057378296, 9169205035462, 34441763801094, 129371640763978

Offset

1,1

Comments

Column 4 of A250387.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +7*a(n-2) -7*a(n-3) +31*a(n-4) +27*a(n-5) -237*a(n-6) -42*a(n-7) +109*a(n-8) -809*a(n-9) +976*a(n-10) +2527*a(n-11) -1891*a(n-12) -83*a(n-13) +2938*a(n-14) -3839*a(n-15) -1155*a(n-16) +1894*a(n-17) -2913*a(n-18) +471*a(n-19) +2319*a(n-20) -198*a(n-21) +36*a(n-22) -216*a(n-24).

Empirical g.f.: 2*x*(210 + 360*x - 106*x^2 + 1137*x^3 - 2269*x^4 - 13879*x^5 - 1808*x^6 + 386*x^7 - 22089*x^8 + 87395*x^9 + 113109*x^10 - 104339*x^11 + 25652*x^12 + 99193*x^13 - 238490*x^14 - 38645*x^15 + 71125*x^16 - 154383*x^17 + 67320*x^18 + 134124*x^19 - 12168*x^20 + 864*x^21 - 3888*x^22 - 12960*x^23) / (1 - 2*x - 7*x^2 + 7*x^3 - 31*x^4 - 27*x^5 + 237*x^6 + 42*x^7 - 109*x^8 + 809*x^9 - 976*x^10 - 2527*x^11 + 1891*x^12 + 83*x^13 - 2938*x^14 + 3839*x^15 + 1155*x^16 - 1894*x^17 + 2913*x^18 - 471*x^19 - 2319*x^20 + 198*x^21 - 36*x^22 + 216*x^24). - Colin Barker, Aug 20 2017

Example

Some solutions for n=5:
..2....4....3....4....2....4....3....0....4....4....4....0....1....0....0....4
..3....0....1....3....4....4....2....1....0....1....1....2....4....4....2....3
..4....3....0....1....3....2....1....0....4....4....4....3....0....2....4....4
..4....1....3....4....2....3....4....3....2....2....0....1....2....4....1....2
..0....4....0....1....0....1....0....3....3....0....3....3....0....1....3....0
..1....1....2....2....0....4....3....0....0....4....4....2....4....0....0....3
..2....2....3....0....2....0....2....0....0....4....4....4....0....3....3....1
..4....0....3....0....3....4....4....4....3....2....0....2....1....2....2....2

Crossrefs

Sequence in context: A281210 A235233 A251084 * A145678 A160372 A171259

Adjacent sequences: A250380 A250381 A250382 * A250384 A250385 A250386

Keyword

nonn

Author

R. H. Hardin, Nov 20 2014

Status

approved