

A221516


Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0.


1



0, 3, 30, 130, 381, 884, 1765, 3174, 5285, 8296, 12429, 17930, 25069, 34140, 45461, 59374, 76245, 96464, 120445, 148626, 181469, 219460, 263109, 312950, 369541, 433464, 505325, 585754, 675405, 774956, 885109, 1006590, 1140149, 1286560
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OFFSET

1,2


COMMENTS

Row 5 of A221515.


LINKS

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


FORMULA

Empirical: a(n) = 1*n^4  1*n^3  10*n^2 + 33*n  34 for n>3.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: x^2*(3 + 15*x + 10*x^2 + x^3  6*x^4 + 2*x^5  x^6) / (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
..3....6....3....6....4....2....3....2....5....4....4....6....2....6....6....2
..5....2....4....2....6....3....3....0....6....1....0....0....0....4....5....3
..4....4....6....6....5....5....0....6....0....0....5....4....4....2....1....6
..6....6....4....4....0....3....4....1....2....5....0....2....0....4....4....0


CROSSREFS

Cf. A221515.
Sequence in context: A100259 A031205 A225018 * A174774 A020874 A161806
Adjacent sequences: A221513 A221514 A221515 * A221517 A221518 A221519


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 18 2013


STATUS

approved



