A269693 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by plus or minus one modulo n+1.

66, 1347, 13168, 69405, 260616, 786079, 2031072, 4674393, 9831160, 19235931, 35471184, 62246197, 104731368, 169953015, 267253696, 408823089, 610304472, 891481843, 1277052720, 1797491661, 2490009544, 3399613647, 4580273568

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + 7*n^6 + 21*n^5 + 15*n^4 - 13*n^3 - 11*n^2 + 3*n + 1 for n>1.

Conjectures from Colin Barker, Jan 28 2019: (Start)

G.f.: x*(66 + 819*x + 4240*x^2 - 1919*x^3 + 3268*x^4 - 2323*x^5 + 1184*x^6 - 337*x^7 + 42*x^8) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.

(End)

Example

Some solutions for n=3:
..1. .1. .0. .0. .3. .0. .3. .3. .3. .0. .0. .3. .0. .2. .0. .2
..3. .0. .3. .0. .1. .2. .1. .2. .0. .3. .3. .2. .3. .2. .1. .0
..2. .3. .2. .1. .2. .3. .3. .2. .2. .0. .2. .3. .2. .2. .0. .1
..3. .1. .3. .3. .3. .3. .0. .3. .2. .2. .2. .3. .3. .2. .0. .3
..2. .2. .2. .0. .1. .1. .1. .0. .0. .1. .2. .3. .1. .2. .2. .1
..3. .0. .3. .1. .2. .0. .1. .0. .1. .2. .3. .1. .3. .0. .0. .0
..0. .0. .2. .3. .1. .3. .3. .0. .2. .2. .2. .3. .3. .3. .0. .0

Crossrefs

Row 7 of A269690.

Sequence in context: A240004 A231287 A263522 * A278850 A104673 A251047

Adjacent sequences: A269690 A269691 A269692 * A269694 A269695 A269696

Keyword

nonn

Author

R. H. Hardin, Mar 03 2016

Status

approved