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A224671 Number of (n+1) X 4 0..2 matrices with each 2 X 2 subblock idempotent. 1
41, 76, 108, 170, 257, 398, 617, 967, 1525, 2421, 3862, 6185, 9934, 15990, 25778, 41604, 67199, 108600, 175575, 283929, 459235, 742871, 1201788, 1944315, 3145732, 5089648, 8234952, 13324142, 21558605, 34882226, 56440277, 91321915, 147761569 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 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) for n>6.

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

G.f.: x*(41 - 88*x + 9*x^2 + 77*x^3 - 41*x^4 + x^5) / ((1 - x)^3*(1 - x - x^2)).

a(n) = 5 + (2^(-1-n)*((1-sqrt(5))^n*(-19+29*sqrt(5)) + (1+sqrt(5))^n*(19+29*sqrt(5)))) / sqrt(5) + 4*(1+n) + (1+n)*(2+n)/2 for n>1.

(End)

EXAMPLE

Some solutions for n=3:

..1..1..1..0....1..0..1..0....1..1..1..2....0..0..0..0....1..1..0..0

..0..0..0..0....1..0..1..0....0..0..0..0....0..0..0..0....0..0..0..0

..1..1..1..1....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..0

..0..0..0..0....0..0..1..0....0..0..0..1....0..0..0..0....0..0..0..1

CROSSREFS

Sequence in context: A142038 A213047 A269426 * A044107 A044488 A335482

Adjacent sequences:  A224668 A224669 A224670 * A224672 A224673 A224674

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 14 2013

STATUS

approved

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Last modified September 23 19:48 EDT 2021. Contains 347617 sequences. (Running on oeis4.)