A224328 Number of idempotent n X n 0..3 matrices of rank n-1.

1, 14, 93, 508, 2555, 12282, 57337, 262136, 1179639, 5242870, 23068661, 100663284, 436207603, 1879048178, 8053063665, 34359738352, 146028888047, 618475290606, 2611340115949, 10995116277740, 46179488366571, 193514046488554

Offset: 1

Author

R. H. Hardin, formula via M. F. Hasler _William J. Keith_ and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013

Keywords

• nonn
• easy

Comments

Column 3 of A224333

Examples

			Some solutions for n=3
..0..1..3....1..0..0....0..0..0....0..0..0....0..1..0....1..3..0....1..0..0
..0..1..0....0..0..1....0..1..0....2..1..0....0..1..0....0..0..0....0..1..0
..0..0..1....0..0..1....1..0..1....0..0..1....0..0..1....0..3..1....0..3..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (10,-33,40,-16).

Formula

a(n) = n*(2*4^(n-1)-1).

a(n) = 10*a(n-1) -33*a(n-2) +40*a(n-3) -16*a(n-4).

G.f.: -x*(-1-4*x+14*x^2) / ( (4*x-1)^2*(x-1)^2 ). - R. J. Mathar, Oct 21 2014