A224331 Number of idempotent n X n 0..6 matrices of rank n-1.

1, 26, 291, 2740, 24005, 201678, 1647079, 13176680, 103766409, 807072130, 6214455467, 47455841820, 359873467213, 2712892291382, 20346692185455, 151921968318160, 1129919639366417, 8374698503539434, 61879716720597043

Offset

1,2

Comments

Column 6 of A224333.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Index entries for linear recurrences with constant coefficients, signature (16,-78,112,-49).

Formula

a(n) = n*(2*7^(n-1)-1).

a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4).

G.f.: x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2). - Colin Barker, Aug 29 2018

Example

Some solutions for n=3:
..1..5..0....0..3..6....1..0..0....0..0..0....1..0..0....1..0..0....0..0..0
..0..0..0....0..1..0....0..1..0....6..1..0....0..1..0....0..1..0....2..1..0
..0..2..1....0..0..1....0..0..0....4..0..1....1..6..0....3..4..0....3..0..1

Mathematica

Table[n*(2*7^(n-1)-1), {n, 1, 40}] (* or *)
CoefficientList[Series[(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) , {x, 0, 40}], x] (* Stefano Spezia, Aug 29 2018 *)

Prog

(PARI) Vec(x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018

Crossrefs

Cf. A224333.

Sequence in context: A336732 A227332 A020925 * A125414 A208600 A010831

Adjacent sequences: A224328 A224329 A224330 * A224332 A224333 A224334

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