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A269620 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1. 1
15, 78, 249, 612, 1275, 2370, 4053, 6504, 9927, 14550, 20625, 28428, 38259, 50442, 65325, 83280, 104703, 130014, 159657, 194100, 233835, 279378, 331269, 390072, 456375, 530790, 613953, 706524, 809187, 922650, 1047645, 1184928, 1335279 (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^4 + 4*n^3 + 5*n^2 + 5*n.

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

G.f.: 3*x*(5 + x + 3*x^2 - x^3) / (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:

..2. .5. .6. .8. .5. .2. .1. .4. .1. .5. .5. .6. .0. .5. .7. .2

..2. .7. .2. .7. .2. .2. .0. .6. .0. .1. .6. .0. .3. .6. .1. .5

..6. .5. .7. .0. .2. .3. .6. .7. .0. .5. .1. .2. .5. .2. .7. .2

..3. .2. .6. .0. .5. .8. .0. .6. .7. .6. .2. .2. .4. .4. .2. .4

CROSSREFS

Row 4 of A269619.

Sequence in context: A128272 A180579 A081591 * A269436 A044202 A044583

Adjacent sequences:  A269617 A269618 A269619 * A269621 A269622 A269623

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2016

STATUS

approved

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Last modified May 12 04:27 EDT 2021. Contains 343810 sequences. (Running on oeis4.)