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A224543
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Number of (n+1) X (n+1) 0..1 matrices with each 2 X 2 subblock idempotent.
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1
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8, 32, 78, 196, 428, 916, 1858, 3678, 7096, 13458, 25150, 46466, 85028, 154356, 278298, 498792, 889320, 1578248, 2789166, 4910498, 8615348, 15067462, 26274538, 45693286
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OFFSET
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1,1
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COMMENTS
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Diagonal of A224550.
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LINKS
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Table of n, a(n) for n=1..24.
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FORMULA
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Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9).
Empirical g.f.: 2*x*(4 - 8*x - 9*x^2 + 36*x^3 - 34*x^4 + 11*x^5 - 5*x^6 + 7*x^7 + x^8) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Aug 30 2018
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EXAMPLE
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Some solutions for n=3:
..0..1..0..0....0..0..0..0....1..1..0..0....0..0..0..0....0..0..0..0
..0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0....1..1..1..1
..0..1..0..1....0..0..0..0....0..0..0..1....1..1..1..1....0..0..0..0
..0..1..0..1....0..1..1..1....0..0..0..1....0..0..0..0....0..1..1..1
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CROSSREFS
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Cf. A224550.
Sequence in context: A009245 A018842 A139098 * A211633 A130809 A333174
Adjacent sequences: A224540 A224541 A224542 * A224544 A224545 A224546
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Apr 10 2013
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STATUS
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approved
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