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

Author

R. H. Hardin, Mar 01 2015

Keywords

• nonn

Comments

Row 1 of A255660.

Examples

			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
		

Links

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

Crossrefs

Cf. A255660.

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