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A224327
Number of idempotent n X n 0..2 matrices of rank n-1.
1
1, 10, 51, 212, 805, 2910, 10199, 34984, 118089, 393650, 1299067, 4251516, 13817453, 44641030, 143489055, 459165008, 1463588497, 4649045850, 14721978563, 46490458660, 146444944821, 460255540910, 1443528741991, 4518872583672
OFFSET
1,2
COMMENTS
Column 2 of A224333.
FORMULA
a(n) = n*(2*3^(n-1)-1).
a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4).
G.f.: x*(1 + 2*x - 7*x^2) / ((1 - x)^2*(1 - 3*x)^2). - Colin Barker, Aug 29 2018
EXAMPLE
Some solutions for n=3:
..1..0..0....1..0..0....1..0..0....1..1..0....1..0..0....1..0..1....1..0..0
..0..0..2....0..1..0....0..1..2....0..0..0....0..0..1....0..1..2....0..1..0
..0..0..1....0..0..0....0..0..0....0..2..1....0..0..1....0..0..0....1..0..0
CROSSREFS
Cf. A224333.
Sequence in context: A069038 A213563 A030183 * A219573 A135242 A362673
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, formula via M. F. Hasler William J. Keith and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013
STATUS
approved