A258725 Number of length n+3 0..3 arrays with at most one downstep in every 3 consecutive neighbor pairs.

190, 608, 2028, 6552, 20955, 68120, 220854, 711432, 2300008, 7446144, 24054120, 77722752, 251353605, 812507404, 2625900876, 8488906820, 27442096806, 88701621392, 286727659260, 926874621576, 2996101722471, 9684839732128

Offset

1,1

Comments

Column 3 of A258730.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +20*a(n-3) -34*a(n-4) +24*a(n-5) -16*a(n-6) +8*a(n-7) -a(n-8).

Empirical g.f.: x*(190 - 152*x + 736*x^2 - 1712*x^3 + 1215*x^4 - 836*x^5 + 464*x^6 - 60*x^7) / (1 - 4*x + 6*x^2 - 20*x^3 + 34*x^4 - 24*x^5 + 16*x^6 - 8*x^7 + x^8). - Colin Barker, Jan 26 2018

Example

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

Crossrefs

Cf. A258730.

Sequence in context: A051979 A097647 A248995 * A232387 A296521 A223462

Adjacent sequences: A258722 A258723 A258724 * A258726 A258727 A258728

Keyword

nonn

Author

R. H. Hardin, Jun 08 2015

Status

approved