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A224670 Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent 1
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 (list; graph; refs; listen; history; text; internal format)
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 A034025

Adjacent sequences:  A224667 A224668 A224669 * A224671 A224672 A224673

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 14 2013

STATUS

approved

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)