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A224671
Number of (n+1) X 4 0..2 matrices with each 2 X 2 subblock idempotent.
1
41, 76, 108, 170, 257, 398, 617, 967, 1525, 2421, 3862, 6185, 9934, 15990, 25778, 41604, 67199, 108600, 175575, 283929, 459235, 742871, 1201788, 1944315, 3145732, 5089648, 8234952, 13324142, 21558605, 34882226, 56440277, 91321915, 147761569
OFFSET
1,1
COMMENTS
Column 3 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) for n>6.
Conjectures from Colin Barker, Feb 17 2018: (Start)
G.f.: x*(41 - 88*x + 9*x^2 + 77*x^3 - 41*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)).
a(n) = 5 + (2^(-1-n)*((1-sqrt(5))^n*(-19+29*sqrt(5)) + (1+sqrt(5))^n*(19+29*sqrt(5)))) / sqrt(5) + 4*(1+n) + (1+n)*(2+n)/2 for n>1.
(End)
EXAMPLE
Some solutions for n=3:
..1..1..1..0....1..0..1..0....1..1..1..2....0..0..0..0....1..1..0..0
..0..0..0..0....1..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0
..1..1..1..1....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..1
CROSSREFS
Sequence in context: A142038 A213047 A269426 * A044107 A044488 A335482
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 14 2013
STATUS
approved