A224722 Number of (n+3) X 5 0..2 matrices with each 4 X 4 subblock idempotent.

1623, 1920, 2493, 2863, 3123, 4129, 5711, 7604, 9713, 12764, 17344, 23754, 32224, 43673, 59650, 81969, 112701, 154811, 212841, 293114, 404063, 557046, 767994, 1059140, 1461174, 2016107, 2781924, 3838807, 5297655, 7311353, 10090799

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) + a(n-11) - a(n-12) for n>15.

Empirical g.f.: x*(1623 - 1326*x + 276*x^2 - 1826*x^3 - 2030*x^4 + 1499*x^5 - 70*x^6 + 3500*x^7 - 86*x^8 - 240*x^9 - 200*x^10 - 1693*x^11 + 508*x^12 + 48*x^13 + 5*x^14) / ((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2)*(1 - x - x^4)). - Colin Barker, Sep 03 2018

Example

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

Crossrefs

Column 2 of A224728.

Sequence in context: A269274 A020418 A347039 * A045288 A204726 A022060

Adjacent sequences: A224719 A224720 A224721 * A224723 A224724 A224725

Keyword

nonn

Author

R. H. Hardin, Apr 16 2013

Status

approved