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A258733 Number of length n+3 0..3 arrays with at most one downstep in every n consecutive neighbor pairs. 1
256, 840, 2028, 4184, 7834, 13720, 22866, 36656, 56925, 86064, 127140, 184032, 261584, 365776, 503914, 684840, 919163, 1219512, 1600812, 2080584, 2679270, 3420584, 4331890, 5444608, 6794649, 8422880, 10375620, 12705168, 15470364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (1/5040)*n^7 + (7/720)*n^6 + (29/144)*n^5 + (305/144)*n^4 + (1027/45)*n^3 + (16267/180)*n^2 + (2425/21)*n + 24 for n>1.

Empirical g.f.: x*(256 - 1208*x + 2476*x^2 - 2856*x^3 + 2026*x^4 - 904*x^5 + 242*x^6 - 32*x^7 + x^8) / (1 - x)^8. - Colin Barker, Jan 26 2018

EXAMPLE

Some solutions for n=4:

..3....0....0....2....3....1....1....1....1....0....0....0....3....2....0....0

..0....3....0....2....2....0....3....1....1....0....0....2....2....1....1....2

..0....3....2....2....2....1....2....2....1....0....0....2....2....2....1....3

..1....3....2....0....2....1....2....3....2....2....1....2....2....3....1....3

..2....1....0....1....3....1....2....3....0....2....1....3....2....3....0....3

..2....1....0....1....0....2....2....3....0....0....1....0....0....0....2....1

..2....3....2....3....1....2....0....1....1....0....3....2....3....3....3....2

CROSSREFS

Row 3 of A258730.

Sequence in context: A203450 A188248 A253822 * A209381 A236987 A236980

Adjacent sequences:  A258730 A258731 A258732 * A258734 A258735 A258736

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 08 2015

STATUS

approved

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Last modified May 29 08:07 EDT 2022. Contains 354122 sequences. (Running on oeis4.)