

A221543


Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.


1



3, 22, 103, 303, 716, 1455, 2658, 4487, 7128, 10791, 15710, 22143, 30372, 40703, 53466, 69015, 87728, 110007, 136278, 166991, 202620, 243663, 290642, 344103, 404616, 472775, 549198, 634527, 729428, 834591, 950730, 1078583, 1218912
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OFFSET

1,1


COMMENTS

Row 5 of A221542.


LINKS

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


FORMULA

Empirical: a(n) = 1*n^4 + 1*n^3  3*n^2 + 10*n  9 for n>3.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(3 + 7*x + 23*x^2  22*x^3 + 26*x^4  18*x^5 + 6*x^6  x^7) / (1  x)^5.
a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) for n>8.
(End)


EXAMPLE

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


CROSSREFS

Cf. A221542.
Sequence in context: A254332 A009029 A009032 * A309000 A061182 A143552
Adjacent sequences: A221540 A221541 A221542 * A221544 A221545 A221546


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 19 2013


STATUS

approved



