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

Author

R. H. Hardin, Feb 16 2016

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 4 of A268956.

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