

A245158


Number of length n 0..3 arrays with new values introduced in order from both ends.


1



1, 1, 2, 4, 9, 23, 65, 199, 653, 2275, 8313, 31439, 121637, 477307, 1888721, 7509799, 29940861, 119550419, 477742889, 1909988479, 7637856725, 30546970411, 122178444417, 488693854679, 1954733475629, 7818845822083, 31275198738905
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OFFSET

1,3


LINKS

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


FORMULA

Empirical: a(n) = 10*a(n1)  37*a(n2) + 64*a(n3)  52*a(n4) + 16*a(n5) for n>6.
Conjectures from Colin Barker, Nov 03 2018: (Start)
G.f.: x*(1  9*x + 29*x^2  43*x^3 + 31*x^4  11*x^5) / ((1  x)^2*(1  2*x)^2*(1  4*x)).
a(n) = (64  27*2^(2+n) + 4^n + 12*(32+3*2^n)*n) / 576 for n>1.
(End)


EXAMPLE

Some solutions for n=7:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....1....1....1....1....1....1....1....0....0....1....1....1
..0....0....0....1....1....2....0....2....2....0....0....1....0....0....1....2
..0....1....0....1....0....0....1....2....1....2....2....0....0....0....2....1
..1....2....0....2....1....2....1....1....0....1....1....1....0....0....0....1
..0....1....0....1....0....1....0....0....0....1....0....0....0....1....1....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0


CROSSREFS

Column 3 of A245163.
Sequence in context: A092668 A164039 A014137 * A245159 A245160 A245161
Adjacent sequences: A245155 A245156 A245157 * A245159 A245160 A245161


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jul 12 2014


STATUS

approved



