A269436 Number of length-4 0..n arrays with no repeated value greater than the previous repeated value.

15, 78, 250, 615, 1281, 2380, 4068, 6525, 9955, 14586, 20670, 28483, 38325, 50520, 65416, 83385, 104823, 130150, 159810, 194271, 234025, 279588, 331500, 390325, 456651, 531090, 614278, 706875, 809565, 923056, 1048080, 1185393, 1335775

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 + (11/2)*n^2 + (7/2)*n + 1.

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

G.f.: x*(15 + 3*x + 10*x^2 - 5*x^3 + x^4) / (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:
..7. .8. .1. .4. .8. .5. .6. .6. .7. .0. .7. .7. .8. .5. .5. .0
..6. .3. .6. .3. .5. .3. .2. .4. .2. .7. .6. .1. .3. .3. .7. .3
..3. .8. .5. .0. .4. .7. .2. .7. .4. .7. .7. .2. .5. .0. .2. .4
..7. .2. .7. .0. .2. .1. .3. .4. .0. .8. .4. .6. .5. .0. .8. .1

Crossrefs

Row 4 of A269435.

Sequence in context: A180579 A081591 A269620 * A044202 A044583 A212746

Adjacent sequences: A269433 A269434 A269435 * A269437 A269438 A269439

Keyword

nonn

Author

R. H. Hardin, Feb 26 2016

Status

approved