A205338 Number of length n+1 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than 5.

0, 5, 20, 160, 1130, 8927, 71630, 594405, 5025740, 43243674, 377127756, 3327001441, 29634744950, 266164547110, 2407763862342, 21918167505714, 200631620380132, 1845576127894008, 17052050519557200, 158176470846492722

Offset

1,2

Comments

Column 5 of A205341.

Links

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

Formula

a(n) = Sum_{i=1..n}((Sum_{l=0..i}(binomial(i,l)*(Sum_{j=0..(5*(i-l))/11}((-1)^j*binomial(i-l,j)*binomial(-l+5*(-l-2*j+i)-j+i-1,5*(-l-2*j+i)-j)))*(-1)^l))*a(n-i))/n, a(0)=1. - Vladimir Kruchinin, Apr 07 2017

Example

Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..5....5....5....2....5....5....4....2....3....2....2....2....4....1....3....1
..8....6...10....3....8....4....6....1....5....5....6....5....7....4....1....4
..3....9....9....0....5....0....2....5....0....4....1....3....4....5....2....7
..1....4....5....3....2....2....3....2....1....3....4....4....2....3....1....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Prog

(Maxima)
a(n):=if n=0 then 1 else sum((sum(binomial(i, l)*(sum((-1)^j*binomial(i-l, j)*binomial(-l+5*(-l-2*j+i)-j+i-1, 5*(-l-2*j+i)-j), j, 0, (5*(i-l))/11))*(-1)^l, l, 0, i))*a(n-i), i, 1, n)/n; /* Vladimir Kruchinin, Apr 07 2017 */

Crossrefs

Sequence in context: A133667 A354848 A318433 * A197857 A197741 A189317

Adjacent sequences: A205335 A205336 A205337 * A205339 A205340 A205341

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved