A268945 Number of length-4 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

10, 63, 220, 565, 1206, 2275, 3928, 6345, 9730, 14311, 20340, 28093, 37870, 49995, 64816, 82705, 104058, 129295, 158860, 193221, 232870, 278323, 330120, 388825, 455026, 529335, 612388, 704845, 807390, 920731, 1045600, 1182753, 1332970

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 + 3*n^2 + n + 1.

Conjectures from Colin Barker, Jan 17 2019: (Start)

G.f.: x*(10 + 13*x + 5*x^2 - 5*x^3 + x^4) / (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=9:
..9. .3. .4. .0. .0. .7. .3. .6. .2. .7. .3. .0. .7. .6. .5. .7
..2. .7. .5. .9. .0. .5. .4. .7. .8. .8. .9. .8. .0. .3. .7. .2
..6. .2. .3. .7. .8. .9. .9. .7. .3. .6. .6. .8. .8. .8. .9. .7
..2. .5. .2. .4. .9. .7. .3. .2. .5. .0. .2. .9. .7. .1. .1. .9

Crossrefs

Row 4 of A268944.

Sequence in context: A027254 A370764 A159240 * A055368 A278802 A077616

Adjacent sequences: A268942 A268943 A268944 * A268946 A268947 A268948

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved