A224739 Number of (n+1) X 3 0..1 matrices with each 2 X 2 permanent equal.

38, 152, 565, 2326, 9554, 40297, 170754, 728996, 3120401, 13387658, 57499978, 247151833, 1062764258, 4571134864, 19664166357, 84599301422, 363983008394, 1566063674345, 6738231845242, 28992616966540, 124747487937041

Offset

1,1

Links

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

Robert Israel, Maple-assisted proof of empirical recurrence

Formula

Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 34*a(n-3) + 59*a(n-4) + 27*a(n-5) - 87*a(n-6) + 36*a(n-7).

Empirical g.f.: x*(38 - 114*x - 233*x^2 + 727*x^3 + 153*x^4 - 1083*x^5 + 504*x^6) / ((1 - x)*(1 - 5*x + 3*x^2)*(1 - 3*x^2)*(1 - x - 4*x^2)). - Colin Barker, Sep 05 2018

Empirical recurrence confirmed (see link). - Robert Israel, Jun 18 2019

Example

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

Crossrefs

Column 2 of A224745.

Sequence in context: A164093 A158064 A251253 * A135176 A318625 A281208

Adjacent sequences: A224736 A224737 A224738 * A224740 A224741 A224742

Keyword

nonn

Author

R. H. Hardin, Apr 17 2013

Status

approved