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

1,1

Comments

Column 2 of A224676.

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)

Example

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

Crossrefs

Sequence in context: A031472 A045210 A169860 * A045195 A232438 A360017

Adjacent sequences: A224667 A224668 A224669 * A224671 A224672 A224673

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved