A269431 Number of length-n 0..4 arrays with no repeated value greater than the previous repeated value.

5, 25, 125, 615, 2995, 14455, 69235, 329430, 1558430, 7334806, 34364270, 160340610, 745362730, 3453222850, 15949215754, 73454841775, 337413819915, 1546145183895, 7068979186035, 32251365241137, 146853223312325, 667445619383425

Offset

1,1

Links

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

Formula

Empirical: a(n) = 20*a(n-1) - 155*a(n-2) + 560*a(n-3) - 810*a(n-4) - 136*a(n-5) + 810*a(n-6) + 560*a(n-7) + 155*a(n-8) + 20*a(n-9) + a(n-10).

Empirical g.f.: x*(5 - 75*x + 400*x^2 - 810*x^3 + 120*x^4 + 810*x^5 + 560*x^6 + 155*x^7 + 20*x^8 + x^9) / (1 - 4*x - x^2)^5. - Colin Barker, Jan 21 2019

Example

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

Crossrefs

Column 4 of A269435.

Sequence in context: A126642 A269615 A269579 * A269686 A269490 A370144

Adjacent sequences: A269428 A269429 A269430 * A269432 A269433 A269434

Keyword

nonn

Author

R. H. Hardin, Feb 26 2016

Status

approved