A269413 Number of length-7 0..n arrays with no repeated value greater than or equal to the previous repeated value.

20, 957, 10132, 56890, 223320, 695135, 1837752, 4302612, 9168780, 18124865, 33696300, 59523022, 100692592, 164133795, 259075760, 397577640, 595133892, 871360197, 1250765060, 1763612130, 2446878280, 3345312487, 4512600552

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + 7*n^6 + 11*n^5 + (8/3)*n^4 - (11/6)*n^3 + (1/3)*n^2 - (1/6)*n.

Conjectures from Colin Barker, Jan 21 2019: (Start)

G.f.: x*(20 + 797*x + 3036*x^2 + 1510*x^3 - 296*x^4 - 27*x^5) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Row 7 of A269409.

Sequence in context: A354814 A066798 A072035 * A274764 A069578 A269644

Adjacent sequences: A269410 A269411 A269412 * A269414 A269415 A269416

Keyword

nonn

Author

R. H. Hardin, Feb 25 2016

Status

approved