A268952 Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

1, 2, 4, 12, 40, 153, 634, 2785, 12634, 58409, 272738, 1280233, 6024682, 28383609, 133772018, 630473513, 2970963898, 13996752665, 65924951490, 310433985929, 1461486107146, 6879181490937, 32374728610962, 152339562845289

Offset

1,2

Links

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

Formula

Empirical: a(n) = 11*a(n-1) -31*a(n-2) -41*a(n-3) +268*a(n-4) -90*a(n-5) -692*a(n-6) +512*a(n-7) +576*a(n-8) -512*a(n-9) for n>11.

Empirical g.f.: x*(1 - 9*x + 13*x^2 + 71*x^3 - 154*x^4 - 197*x^5 + 483*x^6 + 210*x^7 - 546*x^8 - 24*x^9 + 192*x^10) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 2*x^2)*(1 - x - 4*x^2)*(1 - 3*x - 8*x^2)). - Colin Barker, Jan 17 2019

Example

Some solutions for n=8:
..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0
..1. .0. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .0. .1. .1. .1
..2. .1. .1. .2. .2. .2. .1. .2. .0. .2. .0. .2. .1. .0. .0. .2
..1. .2. .2. .3. .1. .3. .2. .2. .2. .1. .2. .1. .0. .2. .2. .0
..3. .0. .1. .4. .2. .2. .1. .3. .1. .3. .0. .3. .1. .2. .3. .1
..4. .1. .3. .0. .0. .4. .2. .3. .1. .1. .3. .0. .2. .3. .4. .1
..2. .2. .4. .1. .1. .3. .1. .4. .3. .0. .3. .3. .2. .4. .2. .2
..0. .2. .0. .3. .0. .1. .0. .4. .2. .2. .1. .2. .1. .0. .1. .0

Crossrefs

Column 4 of A268956.

Sequence in context: A211965 A119430 A074034 * A215072 A326513 A268953

Adjacent sequences: A268949 A268950 A268951 * A268953 A268954 A268955

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved