A224672 Number of (n+1) X 5 0..2 matrices with each 2 X 2 subblock idempotent.

70, 123, 170, 260, 381, 573, 864, 1322, 2043, 3191, 5026, 7972, 12713, 20357, 32696, 52630, 84851, 136951, 221214, 357516, 578017, 934753, 1511920, 2445750, 3956671, 6401343, 10356854, 16756952, 27112473, 43868001, 70978956, 114845342

Offset

1,1

Comments

Column 4 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.

Empirical g.f.: x*(70 - 157*x + 28*x^2 + 125*x^3 - 72*x^4 + 3*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Feb 17 2018

Example

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

Crossrefs

Sequence in context: A357670 A185817 A260573 * A039542 A024748 A024756

Adjacent sequences: A224669 A224670 A224671 * A224673 A224674 A224675

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved