A258734 - OEIS

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

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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.