

A221544


Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1, starting with 0.


1



5, 54, 364, 1386, 4018, 9665, 20386, 39007, 69242, 115813, 184570, 282611, 418402, 601897, 844658, 1159975, 1562986, 2070797, 2702602, 3479803, 4426130, 5567761, 6933442, 8554607, 10465498, 12703285, 15308186, 18323587, 21796162, 25775993
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OFFSET

1,1


COMMENTS

Row 6 of A221542.


LINKS

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


FORMULA

Empirical: a(n) = 1*n^5 + 2*n^4  6*n^3 + 21*n^2  31*n + 23 for n>4.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(5 + 24*x + 115*x^2  88*x^3 + 157*x^4  153*x^5 + 87*x^6  34*x^7 + 8*x^8  x^9) / (1  x)^6.
a(n) = 6*a(n1)  15*a(n2) + 20*a(n3)  15*a(n4) + 6*a(n5)  a(n6) for n>10.
(End)


EXAMPLE

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


CROSSREFS

Cf. A221542.
Sequence in context: A275261 A208429 A275353 * A268882 A229298 A087125
Adjacent sequences: A221541 A221542 A221543 * A221545 A221546 A221547


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 19 2013


STATUS

approved



