A224667 Number of 5 X 5 0..n matrices with each 2 X 2 subblock idempotent.

196, 260, 332, 412, 500, 596, 700, 812, 932, 1060, 1196, 1340, 1492, 1652, 1820, 1996, 2180, 2372, 2572, 2780, 2996, 3220, 3452, 3692, 3940, 4196, 4460, 4732, 5012, 5300, 5596, 5900, 6212, 6532, 6860, 7196, 7540, 7892, 8252, 8620, 8996, 9380, 9772, 10172

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*n^2 + 52*n + 140.

Conjectures from Colin Barker, Sep 02 2018: (Start)

G.f.: 4*x*(49 - 82*x + 35*x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)

Example

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

Crossrefs

Row 5 of A224665.

Sequence in context: A248021 A378792 A151713 * A118781 A119667 A023108

Adjacent sequences: A224664 A224665 A224666 * A224668 A224669 A224670

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved