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

1,2

Comments

Column 3 of A224333

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

Example

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

Crossrefs

Sequence in context: A060217 A113776 A202901 * A241396 A101383 A044265

Adjacent sequences: A224325 A224326 A224327 * A224329 A224330 A224331

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