A224669 Number of (n+1) X 2 0..2 matrices with each 2 X 2 subblock idempotent.

12, 25, 41, 70, 115, 189, 308, 501, 813, 1318, 2135, 3457, 5596, 9057, 14657, 23718, 38379, 62101, 100484, 162589, 263077, 425670, 688751, 1114425, 1803180, 2917609, 4720793, 7638406, 12359203, 19997613, 32356820, 52354437, 84711261, 137065702

Offset

1,1

Comments

Column 1 of A224676.

Links

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

Formula

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

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

G.f.: x*(12 + x - 9*x^2) / ((1 - x)*(1 - x - x^2)).

a(n) = -4 + (2^(-1-n)*((1-sqrt(5))^n*(-19+13*sqrt(5)) + (1+sqrt(5))^n*(19+13*sqrt(5)))) / sqrt(5).

(End)

Example

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

Crossrefs

Sequence in context: A132754 A250666 A363378 * A164577 A195143 A280321

Adjacent sequences: A224666 A224667 A224668 * A224670 A224671 A224672

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved