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

Author

R. H. Hardin, Apr 14 2013

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 4 of A224665.

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)