A269437 Number of length-5 0..n arrays with no repeated value greater than the previous repeated value.

28, 222, 964, 2995, 7536, 16408, 32152, 58149, 98740, 159346, 246588, 368407, 534184, 754860, 1043056, 1413193, 1881612, 2466694, 3188980, 4071291, 5138848, 6419392, 7943304, 9743725, 11856676, 14321178, 17179372, 20476639, 24261720

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^5 + 5*n^4 + (17/2)*n^3 + 8*n^2 + (9/2)*n + 1.

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

G.f.: x*(28 + 54*x + 52*x^2 - 19*x^3 + 6*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Row 5 of A269435.

Sequence in context: A297614 A249710 A269621 * A236355 A133071 A339137

Adjacent sequences: A269434 A269435 A269436 * A269438 A269439 A269440

Keyword

nonn

Author

R. H. Hardin, Feb 26 2016

Status

approved