A258734 Number of length n+4 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

1024, 3136, 6552, 12549, 21860, 35704, 55660, 83758, 122584, 175400, 246280, 340263, 463524, 623564, 829420, 1091896, 1423816, 1840300, 2359064, 3000745, 3789252, 4752144, 5921036, 7332034, 9026200, 11050048, 13456072, 16303307

Offset

1,1

Comments

Row 4 of A258730.

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/90)*n^6 + (19/72)*n^5 + (59/18)*n^4 + (47527/720)*n^3 + (14522/45)*n^2 + (39961/84)*n + 100 for n>2.

Empirical g.f.: x*(1024 - 5056*x + 10136*x^2 - 9403*x^3 + 988*x^4 + 7460*x^5 - 8940*x^6 + 5164*x^7 - 1576*x^8 + 204*x^9) / (1 - x)^8. - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A258730.

Sequence in context: A298607 A366391 A195093 * A195234 A257650 A255664

Adjacent sequences: A258731 A258732 A258733 * A258735 A258736 A258737

Keyword

nonn

Author

R. H. Hardin, Jun 08 2015

Status

approved