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A224543 Number of (n+1) X (n+1) 0..1 matrices with each 2 X 2 subblock idempotent. 1
8, 32, 78, 196, 428, 916, 1858, 3678, 7096, 13458, 25150, 46466, 85028, 154356, 278298, 498792, 889320, 1578248, 2789166, 4910498, 8615348, 15067462, 26274538, 45693286 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Diagonal of A224550.

LINKS

Table of n, a(n) for n=1..24.

FORMULA

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

EXAMPLE

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

CROSSREFS

Cf. A224550.

Sequence in context: A009245 A018842 A139098 * A211633 A130809 A333174

Adjacent sequences:  A224540 A224541 A224542 * A224544 A224545 A224546

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 10 2013

STATUS

approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)