A224675 Number of (n+1) X 8 0..2 matrices with each 2 X 2 subblock idempotent.

308, 470, 617, 864, 1166, 1608, 2230, 3157, 4554, 6711, 10083, 15415, 23907, 37504, 59351, 94538, 151300, 242962, 391084, 630551, 1017808, 1644185, 2657457, 4296729, 6948881, 11239898, 18182645, 29415972, 47591594, 77000076, 124583698

Offset

1,1

Comments

Column 7 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*(308 - 762*x + 277*x^2 + 438*x^3 - 291*x^4 + 15*x^5) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Feb 17 2018

Example

Some solutions for n=3:
  0 0 0 1 0 0 0 0    1 0 1 0 0 0 0 0    1 1 1 1 1 1 1 1
  0 0 0 1 0 0 0 0    1 0 1 0 0 0 0 0    0 0 0 0 0 0 0 0
  0 0 0 1 0 0 0 0    1 0 1 0 0 0 0 0    0 0 0 0 0 0 0 1
  0 0 0 1 0 0 1 1    2 0 1 0 0 0 1 1    0 0 0 0 0 0 0 1

Crossrefs

Sequence in context: A359641 A309566 A118843 * A249552 A237457 A234211

Adjacent sequences: A224672 A224673 A224674 * A224676 A224677 A224678

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved