A224670 Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent.

25, 50, 76, 123, 191, 300, 470, 741, 1173, 1866, 2980, 4775, 7671, 12348, 19906, 32125, 51885, 83846, 135548, 219191, 354515, 573460, 927706, 1500873, 2428261, 3928790, 6356680, 10285071, 16641323, 26925936, 43566770, 70492185, 114058401

Offset: 1

Author

R. H. Hardin, Apr 14 2013

Keywords

• nonn

Comments

Column 2 of A224676.

Examples

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

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5).

Conjectures from Colin Barker, Feb 17 2018: (Start)

G.f.: x*(25 - 50*x + x^2 + 44*x^3 - 21*x^4) / ((1 - x)^3*(1 - x - x^2)).

a(n) = -2 + 2^(1-n)*sqrt(5)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) + 2*(1+n) + (1+n)*(2+n)/2.

(End)