A255661 Number of length n+1 0..3 arrays with at most two downsteps in every n consecutive neighbor pairs.

16, 64, 255, 968, 3340, 10320, 28722, 72920, 171106, 375388, 777452, 1532064, 2891360, 5253680, 9231663, 15745452, 26148180, 42392440, 67248205, 104584680, 159730860, 239932160, 354923400, 517641696, 745106454, 1059497716, 1489468594

Offset

1,1

Comments

Row 1 of A255660.

Links

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

Formula

Empirical: a(n) = (1/39916800)*n^11 + (1/518400)*n^10 + (1/15120)*n^9 + (137/120960)*n^8 + (12461/1209600)*n^7 + (8251/172800)*n^6 + (56011/362880)*n^5 + (14791/25920)*n^4 + (278149/151200)*n^3 + (8149/2100)*n^2 + (2539/462)*n + 4.

Empirical g.f.: x*(16 - 128*x + 543*x^2 - 1388*x^3 + 2394*x^4 - 2964*x^5 + 2683*x^6 - 1760*x^7 + 814*x^8 - 252*x^9 + 47*x^10 - 4*x^11) / (1 - x)^12. - Colin Barker, Jan 21 2018

Example

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

Crossrefs

Cf. A255660.

Sequence in context: A212512 A317235 A375573 * A384784 A073718 A230970

Adjacent sequences: A255658 A255659 A255660 * A255662 A255663 A255664

Keyword

nonn

Author

R. H. Hardin, Mar 01 2015

Status

approved