A269620 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

15, 78, 249, 612, 1275, 2370, 4053, 6504, 9927, 14550, 20625, 28428, 38259, 50442, 65325, 83280, 104703, 130014, 159657, 194100, 233835, 279378, 331269, 390072, 456375, 530790, 613953, 706524, 809187, 922650, 1047645, 1184928, 1335279

Offset: 1

Author

R. H. Hardin, Mar 01 2016

Keywords

• nonn

Examples

			Some solutions for n=8:
..2. .5. .6. .8. .5. .2. .1. .4. .1. .5. .5. .6. .0. .5. .7. .2
..2. .7. .2. .7. .2. .2. .0. .6. .0. .1. .6. .0. .3. .6. .1. .5
..6. .5. .7. .0. .2. .3. .6. .7. .0. .5. .1. .2. .5. .2. .7. .2
..3. .2. .6. .0. .5. .8. .0. .6. .7. .6. .2. .2. .4. .4. .2. .4
		

Links

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

Crossrefs

Row 4 of A269619.

Formula

Empirical: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n.

Conjectures from Colin Barker, Jan 25 2019: (Start)

G.f.: 3*x*(5 + x + 3*x^2 - x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)