A269410 Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value.

9, 63, 222, 570, 1215, 2289, 3948, 6372, 9765, 14355, 20394, 28158, 37947, 50085, 64920, 82824, 104193, 129447, 159030, 193410, 233079, 278553, 330372, 389100, 455325, 529659, 612738, 705222, 807795, 921165, 1046064, 1183248, 1333497

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^4 + 4*n^3 + (7/2)*n^2 + (1/2)*n.

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

G.f.: 3*x*(3 + 6*x - x^2) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=8:
..8. .3. .1. .0. .3. .0. .8. .2. .3. .1. .0. .4. .3. .5. .4. .6
..8. .8. .3. .5. .4. .2. .1. .4. .0. .5. .2. .4. .0. .6. .4. .8
..4. .7. .3. .8. .7. .2. .0. .5. .3. .3. .7. .0. .0. .1. .2. .0
..0. .8. .8. .7. .5. .8. .5. .8. .2. .8. .0. .0. .2. .1. .4. .2

Crossrefs

Row 4 of A269409.

Sequence in context: A299579 A344526 A269641 * A178161 A015669 A202982

Adjacent sequences: A269407 A269408 A269409 * A269411 A269412 A269413

Keyword

nonn

Author

R. H. Hardin, Feb 25 2016

Status

approved