A224721 Number of (n+3) X 4 0..2 matrices with each 4 X 4 subblock idempotent.

2052, 1623, 2471, 3506, 4257, 5737, 8117, 12306, 18187, 26561, 38040, 55162, 80519, 118413, 173641, 254339, 371847, 544345, 797402, 1169025, 1713358, 2510861, 3678903, 5391040, 7900541, 11579142, 16970092, 24870656, 36448737, 53417530

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 2*a(n-5) + 2*a(n-6) - 2*a(n-7) + a(n-8) for n>11.

Empirical g.f.: x*(2052 - 4533*x + 3758*x^2 - 1090*x^3 - 2523*x^4 + 3494*x^5 - 3158*x^6 + 3203*x^7 - 1110*x^8 - 115*x^9 - 4*x^10) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 - x - x^3)). - Colin Barker, Sep 03 2018

Example

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

Crossrefs

Column 1 of A224728.

Sequence in context: A253711 A168176 A224728 * A224720 A320277 A322102

Adjacent sequences: A224718 A224719 A224720 * A224722 A224723 A224724

Keyword

nonn

Author

R. H. Hardin, Apr 16 2013

Status

approved