A224685 Number of (n+4) X 7 0..1 matrices with each 5 X 5 subblock idempotent.

2662, 1494, 1636, 1896, 2136, 2354, 2862, 3701, 4814, 6134, 7579, 9522, 12249, 16025, 21050, 27502, 35816, 46815, 61511, 81188, 107258, 141592, 186820, 246722, 326234, 431740, 571497, 756452, 1001216, 1325438, 1755075, 2324413, 3078635, 4077559

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) - a(n-4) - a(n-7) + a(n-8) -a(n-9) + a(n-10) + a(n-12) - a(n-13) for n>17.

Empirical g.f.: x*(2662 - 3830*x + 1310*x^2 - 2544*x^3 + 1148*x^4 - 164*x^5 + 30*x^6 + 2753*x^7 - 1112*x^8 + 2503*x^9 - 1622*x^10 - 233*x^11 - 2720*x^12 + 1520*x^13 + 221*x^14 + 61*x^15 + 5*x^16) / ((1 - x)^3*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 - x^3)). - Colin Barker, Sep 02 2018

Example

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

Crossrefs

Column 3 of A224690.

Sequence in context: A235733 A235514 A197108 * A167191 A002482 A187293

Adjacent sequences: A224682 A224683 A224684 * A224686 A224687 A224688

Keyword

nonn

Author

R. H. Hardin, Apr 15 2013

Status

approved