A269405 Number of length-n 0..4 arrays with no repeated value greater than or equal to the previous repeated value.

5, 25, 120, 570, 2670, 12380, 56890, 259445, 1175355, 5293671, 23718780, 105781845, 469798125, 2078552055, 9164402118, 40277785365, 176503698495, 771372344695, 3362640467600, 14624384170213, 63463229049585, 274836205944615

Offset

1,1

Links

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

Formula

Empirical: a(n) = 20*a(n-1) - 150*a(n-2) + 460*a(n-3) - 65*a(n-4) - 2472*a(n-5) + 2320*a(n-6) + 6400*a(n-7) - 3840*a(n-8) - 10240*a(n-9) - 4096*a(n-10).

Empirical g.f.: x*(5 - 75*x + 370*x^2 - 380*x^3 - 1905*x^4 + 3265*x^5 + 5590*x^6 - 5865*x^7 - 11455*x^8 - 4339*x^9) / ((1 + x)^4*(1 - 4*x)^6). - Colin Barker, Jan 21 2019

Example

Some solutions for n=7:
..2. .1. .4. .2. .0. .1. .3. .1. .2. .0. .2. .3. .4. .4. .4. .0
..4. .0. .3. .1. .2. .4. .1. .0. .4. .2. .3. .2. .3. .2. .3. .0
..1. .3. .2. .3. .0. .4. .0. .4. .2. .0. .0. .0. .0. .3. .4. .2
..4. .4. .0. .1. .4. .1. .0. .0. .2. .0. .3. .2. .3. .1. .3. .3
..2. .2. .3. .2. .2. .2. .1. .2. .3. .4. .0. .3. .4. .4. .2. .4
..4. .2. .2. .4. .2. .0. .0. .3. .0. .2. .0. .1. .1. .3. .0. .2
..2. .1. .4. .4. .0. .4. .4. .2. .4. .0. .4. .0. .4. .4. .3. .0

Crossrefs

Column 4 of A269409

Sequence in context: A268940 A269636 A269533 * A269674 A269602 A089927

Adjacent sequences: A269402 A269403 A269404 * A269406 A269407 A269408

Keyword

nonn

Author

R. H. Hardin, Feb 25 2016

Status

approved