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A269609 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by one or less. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A196459 A193132

Adjacent sequences:  A269606 A269607 A269608 * A269610 A269611 A269612

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2016

STATUS

approved

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Last modified June 18 08:40 EDT 2021. Contains 345098 sequences. (Running on oeis4.)