A221592 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less.

0, 13, 35, 169, 651, 2715, 11011, 45099, 184063, 752155, 3072247, 12550859, 51270383, 209444163, 855592375, 3495156539, 14277953839, 58326437619, 238267540647, 973339457803, 3976159254687, 16242886662499, 66353319815959, 271057918757755, 1107290419059023

Offset

1,2

Comments

Column 4 of A221596.

Links

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

Sergey Kitaev, Jeffrey Remmel, (a,b)-rectangle patterns in permutations and words, arXiv:1304.4286 [math.CO], 2013.

Index entries for linear recurrences with constant coefficients, signature (3,4,0,6,4,4).

Formula

a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).

G.f.: x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - Colin Barker, Jan 31 2017

Example

Some solutions for n=6
..3....3....2....1....4....4....3....3....3....3....4....4....2....2....3....3
..2....3....1....0....3....3....4....2....4....4....3....3....2....3....2....2
..1....0....4....2....4....2....0....3....4....2....4....2....2....4....3....3
..1....1....4....3....2....1....0....1....3....3....0....0....4....4....0....3
..3....2....2....0....3....0....1....1....3....0....0....0....3....4....1....4
..3....1....3....1....2....0....0....0....3....1....0....1....2....4....1....4

Prog

(PARI) concat(0, Vec(x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6) + O(x^30))) \\ Colin Barker, Jan 31 2017

Crossrefs

Sequence in context: A243383 A242578 A192145 * A135172 A183309 A272108

Adjacent sequences: A221589 A221590 A221591 * A221593 A221594 A221595

Keyword

nonn,easy

Author

R. H. Hardin, Jan 20 2013

Status

approved