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A224332
Number of idempotent n X n 0..7 matrices of rank n-1.
1
1, 30, 381, 4092, 40955, 393210, 3670009, 33554424, 301989879, 2684354550, 23622320117, 206158430196, 1786706395123, 15393162788850, 131941395333105, 1125899906842608, 9570149208162287, 81064793292668910, 684547143360315373
OFFSET
1,2
COMMENTS
Column 7 of A224333.
FORMULA
a(n) = n*(2*8^(n-1)-1).
a(n) = 18*a(n-1) - 97*a(n-2) + 144*a(n-3) - 64*a(n-4).
G.f.: x*(1 + 12*x - 62*x^2) / ((1 - x)^2*(1 - 8*x)^2). - Colin Barker, Aug 29 2018
EXAMPLE
Some solutions for n=3:
..1..0..3....0..0..4....0..3..0....0..0..1....1..0..6....0..7..7....1..0..3
..0..1..3....0..1..0....0..1..0....0..1..0....0..1..4....0..1..0....0..1..6
..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..0..1....0..0..0
MATHEMATICA
Table[n*(2*8^(n-1)-1), {n, 1, 40}] (* Stefano Spezia, Aug 29 2018 *)
PROG
(PARI) Vec(x*(1 + 12*x - 62*x^2) / ((1 - x)^2*(1 - 8*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018
(PARI) a(n) = n*(2*8^(n-1)-1); \\ Altug Alkan, Aug 31 2018
CROSSREFS
Cf. A224333.
Sequence in context: A202074 A251895 A022690 * A280478 A020927 A105468
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