A224666 Number of 4 X 4 0..n matrices with each 2 X 2 subblock idempotent.

78, 108, 142, 180, 222, 268, 318, 372, 430, 492, 558, 628, 702, 780, 862, 948, 1038, 1132, 1230, 1332, 1438, 1548, 1662, 1780, 1902, 2028, 2158, 2292, 2430, 2572, 2718, 2868, 3022, 3180, 3342, 3508, 3678, 3852, 4030, 4212, 4398, 4588, 4782, 4980, 5182

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*n^2 + 24*n + 52.

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

G.f.: 2*x*(39 - 63*x + 26*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:
..1..0..0..0....1..0..0..0....1..1..0..1....1..0..1..0....1..0..0..0
..0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0....1..0..0..0
..0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0....1..0..0..0
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..0....0..0..1..1

Crossrefs

Row 4 of A224665.

Sequence in context: A025378 A370206 A157355 * A161596 A275218 A260364

Adjacent sequences: A224663 A224664 A224665 * A224667 A224668 A224669

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved