A258734 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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.