A269609 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by one or less.

12, 376, 2878, 12570, 40288, 105892, 242226, 499798, 952180, 1702128, 2888422, 4693426, 7351368, 11157340, 16477018, 23757102, 33536476, 46458088, 63281550, 84896458, 112336432, 146793876, 189635458, 242418310, 306906948, 385090912

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 + 11*n^4 - 8*n^3 + n^2 + 3*n - 2.

Conjectures from Colin Barker, Jan 25 2019: (Start)

G.f.: 2*x*(6 + 146*x + 249*x^2 - 50*x^3 - 2*x^4 + 12*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:
..1. .5. .3. .0. .2. .0. .3. .3. .5. .0. .0. .5. .5. .4. .2. .5
..0. .0. .5. .6. .5. .4. .1. .4. .1. .1. .0. .4. .1. .5. .4. .1
..5. .4. .2. .3. .3. .6. .0. .6. .0. .3. .5. .2. .3. .0. .5. .1
..1. .3. .0. .4. .4. .2. .4. .6. .1. .6. .6. .6. .1. .6. .6. .4
..4. .2. .4. .6. .0. .0. .2. .3. .5. .2. .0. .3. .3. .6. .0. .6
..1. .4. .1. .6. .4. .2. .6. .2. .5. .4. .3. .2. .5. .2. .0. .4

Crossrefs

Row 6 of A269606.

Sequence in context: A024298 A177112 A081021 * A251590 A352651 A196459

Adjacent sequences: A269606 A269607 A269608 * A269610 A269611 A269612

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved