A269439 Number of length-7 0..n arrays with no repeated value greater than the previous repeated value.

92, 1722, 13868, 69235, 255576, 767172, 1981512, 4566213, 9621220, 18861326, 34844052, 61247927, 103206208, 167701080, 264023376, 404302857, 604114092, 883162978, 1266058940, 1783177851, 2471620712, 3376273132, 4550970648

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 + 16*n^5 + (71/3)*n^4 + (139/6)*n^3 + (43/3)*n^2 + (35/6)*n + 1.

Conjectures from Colin Barker, Jan 22 2019: (Start)

G.f.: x*(92 + 986*x + 2668*x^2 + 1355*x^3 + 8*x^4 - 76*x^5 + 8*x^6 - x^7) / (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. .0. .2. .1. .4. .0. .3. .4. .0. .1. .2. .0. .4. .3. .4
..2. .2. .1. .0. .2. .4. .1. .1. .3. .3. .4. .1. .4. .0. .0. .1
..0. .4. .0. .2. .1. .3. .2. .0. .4. .2. .3. .3. .2. .1. .2. .2
..0. .1. .4. .3. .2. .4. .3. .4. .2. .3. .0. .1. .0. .4. .4. .3
..4. .1. .4. .3. .4. .2. .3. .0. .2. .1. .2. .0. .3. .1. .1. .0
..2. .0. .1. .2. .3. .1. .2. .0. .3. .3. .0. .1. .3. .4. .2. .3
..3. .1. .4. .4. .2. .4. .0. .3. .2. .0. .3. .3. .1. .1. .3. .4

Crossrefs

Row 7 of A269435.

Sequence in context: A265968 A179798 A232795 * A269623 A265923 A249236

Adjacent sequences: A269436 A269437 A269438 * A269440 A269441 A269442

Keyword

nonn

Author

R. H. Hardin, Feb 26 2016

Status

approved