login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A221575
Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1.
1
6, 57, 342, 1293, 3734, 8991, 19014, 36497, 64998, 109059, 174326, 267669, 397302, 572903, 805734, 1108761, 1496774, 1986507, 2596758, 3348509, 4265046, 5372079, 6697862, 8273313, 10132134, 12310931, 14849334, 17790117, 21179318, 25066359
OFFSET
1,1
COMMENTS
Row 5 of A221573.
LINKS
FORMULA
Empirical: a(n) = 1*n^5 + 1*n^4 - 2*n^3 + 12*n^2 - 15*n + 9 for n>2.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(6 + 21*x + 90*x^2 - 24*x^3 + 56*x^4 - 39*x^5 + 12*x^6 - 2*x^7) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>8.
(End)
EXAMPLE
Some solutions for n=6:
..6....5....2....5....5....0....2....0....1....2....3....0....3....1....1....1
..4....3....0....0....5....3....5....5....1....6....6....6....3....4....3....5
..0....3....1....3....2....0....4....0....3....6....0....3....5....2....3....6
..0....3....6....5....2....0....4....2....4....6....4....1....0....2....0....0
..0....1....2....0....4....2....1....0....6....6....1....5....3....2....2....0
CROSSREFS
Cf. A221573.
Sequence in context: A181430 A281557 A227813 * A001593 A261740 A296027
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 20 2013
STATUS
approved