A200841 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases or two consecutive decreases.

64, 529, 2356, 7587, 19930, 45465, 93472, 177381, 315844, 533929, 864436, 1349335, 2041326, 3005521, 4321248, 6083977, 8407368, 11425441, 15294868, 20197387, 26342338, 33969321, 43350976, 54795885, 68651596, 85307769, 105199444

Offset

1,1

Comments

Row 4 of A200838.

Links

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

Formula

Empirical: a(n) = (61/360)*n^6 + (93/40)*n^5 + (779/72)*n^4 + (521/24)*n^3 + (1801/90)*n^2 + (239/30)*n + 1.

Conjectures from Colin Barker, Oct 14 2017: (Start)

G.f.: x*(64 + 81*x - 3*x^2 - 36*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Sequence in context: A066430 A115740 A100415 * A247929 A070054 A265636

Adjacent sequences: A200838 A200839 A200840 * A200842 A200843 A200844

Keyword

nonn

Author

R. H. Hardin Nov 23 2011

Status

approved