A224554 Number of (n+2) X 5 0..1 matrices with each 3 X 3 subblock idempotent.

113, 133, 180, 230, 320, 451, 620, 866, 1229, 1746, 2493, 3586, 5178, 7498, 10891, 15855, 23117, 33749, 49321, 72130, 105545, 154505, 226246, 331373, 485430, 711197, 1042059, 1526945, 2237564, 3279010, 4805306, 7042184, 10320470, 15125013

Offset

1,1

Comments

Column 3 of A224559.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 5*a(n-3) - 4*a(n-4) + 3*a(n-5) - a(n-6) for n>8.

Empirical g.f.: x*(113 - 319*x + 326*x^2 - 257*x^3 + 267*x^4 - 156*x^5 + 20*x^6 + 5*x^7) / ((1 - x)^3*(1 - x - x^3)). - Colin Barker, Aug 31 2018

Example

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

Crossrefs

Cf. A224559.

Sequence in context: A344627 A187867 A216288 * A095617 A382766 A139645

Adjacent sequences: A224551 A224552 A224553 * A224555 A224556 A224557

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved