login
A221464
Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.
1
3, 32, 135, 384, 875, 1728, 3087, 5120, 8019, 12000, 17303, 24192, 32955, 43904, 57375, 73728, 93347, 116640, 144039, 176000, 213003, 255552, 304175, 359424, 421875, 492128, 570807, 658560, 756059, 864000, 983103, 1114112, 1257795
OFFSET
1,1
COMMENTS
Row 5 of A221463.
LINKS
FORMULA
Empirical: a(n) = 1*n^4 + 2*n^3.
Conjectures from Colin Barker, Aug 05 2018: (Start)
G.f.: x*(3 + 17*x + 5*x^2 - x^3) / (1 - x)^5.
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>5.
(End)
EXAMPLE
Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..5....6....3....4....4....1....1....4....5....3....4....4....5....6....5....6
..0....6....1....5....5....5....3....5....1....3....0....4....5....4....3....0
..2....5....2....5....5....3....0....3....0....4....0....3....2....0....2....2
..5....0....1....4....2....0....4....5....6....3....1....2....0....6....0....4
CROSSREFS
Cf. A221463.
Sequence in context: A345687 A211224 A213845 * A119940 A004256 A183457
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 17 2013
STATUS
approved