A269438 Number of length-6 0..n arrays with no repeated value greater than the previous repeated value.

51, 622, 3674, 14455, 44021, 112476, 252932, 516189, 976135, 1735866, 2934526, 4754867, 7431529, 11260040, 16606536, 23918201, 33734427, 46698694, 63571170, 85242031, 112745501, 147274612, 190196684, 243069525, 307658351, 385953426

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^6 + 6*n^5 + 12*n^4 + (44/3)*n^3 + (23/2)*n^2 + (29/6)*n + 1.

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

G.f.: x*(51 + 265*x + 391*x^2 + 14*x^3 + 5*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 6 of A269435.

Sequence in context: A319542 A173804 A166820 * A269622 A210055 A020278

Adjacent sequences: A269435 A269436 A269437 * A269439 A269440 A269441

Keyword

nonn

Author

R. H. Hardin, Feb 26 2016

Status

approved