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A224670
Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent
1
25, 50, 76, 123, 191, 300, 470, 741, 1173, 1866, 2980, 4775, 7671, 12348, 19906, 32125, 51885, 83846, 135548, 219191, 354515, 573460, 927706, 1500873, 2428261, 3928790, 6356680, 10285071, 16641323, 26925936, 43566770, 70492185, 114058401
OFFSET
1,1
COMMENTS
Column 2 of A224676.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5).
Conjectures from Colin Barker, Feb 17 2018: (Start)
G.f.: x*(25 - 50*x + x^2 + 44*x^3 - 21*x^4) / ((1 - x)^3*(1 - x - x^2)).
a(n) = -2 + 2^(1-n)*sqrt(5)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) + 2*(1+n) + (1+n)*(2+n)/2.
(End)
EXAMPLE
Some solutions for n=3:
..1..0..2....0..0..0....1..1..1....1..0..0....1..0..0....0..0..0....1..0..0
..0..0..1....0..0..0....0..0..0....0..0..1....0..0..0....0..0..0....0..0..0
..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..0..0
..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....1..1..1....0..0..0
CROSSREFS
Sequence in context: A031472 A045210 A169860 * A045195 A232438 A360017
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 14 2013
STATUS
approved