A200788 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases.

64, 622, 3136, 11100, 31395, 75992, 164004, 324087, 597190, 1039654, 1726660, 2756026, 4252353, 6371520, 9305528, 13287693, 18598188, 25569934, 34594840, 46130392, 60706591, 78933240, 101507580, 129222275, 162973746, 203770854

Offset: 1

Author

R. H. Hardin, Nov 22 2011

Keywords

• nonn

Comments

Row 4 of A200785.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..138

Formula

Empirical: a(n) = (349/720)*n^6 + (321/80)*n^5 + (1883/144)*n^4 + (1013/48)*n^3 + (3139/180)*n^2 + (413/60)*n + 1.

Conjectures from Colin Barker, Oct 15 2017: (Start)

G.f.: x*(64 + 174*x + 126*x^2 - 30*x^3 + 21*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)