A224335 Number of idempotent 4X4 0..n matrices of rank 3.

60, 212, 508, 996, 1724, 2740, 4092, 5828, 7996, 10644, 13820, 17572, 21948, 26996, 32764, 39300, 46652, 54868, 63996, 74084, 85180, 97332, 110588, 124996, 140604, 157460, 175612, 195108, 215996, 238324, 262140, 287492, 314428, 342996, 373244

Offset

1,1

Comments

Row 4 of A224333.

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 8*n^3 + 24*n^2 + 24*n + 4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Colin Barker, Sep 20 2014

G.f.: -4*x*(x^3-5*x^2+7*x-15) / (x-1)^4. - Colin Barker, Sep 20 2014

Example

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

Prog

(PARI) Vec(-4*x*(x^3-5*x^2+7*x-15)/(x-1)^4 + O(x^100)) \\ Colin Barker, Sep 20 2014

Crossrefs

Sequence in context: A378058 A082529 A126248 * A068628 A256985 A075287

Adjacent sequences: A224332 A224333 A224334 * A224336 A224337 A224338

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