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

1,1

Comments

Row 4 of A200785.

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)

Example

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

Crossrefs

Sequence in context: A302086 A229401 A232052 * A250355 A045789 A000525

Adjacent sequences: A200785 A200786 A200787 * A200789 A200790 A200791

Keyword

nonn

Author

R. H. Hardin, Nov 22 2011

Status

approved