A224673 Number of (n+1) X 6 0..2 matrices with each 2 X 2 subblock idempotent

115, 191, 257, 381, 542, 793, 1166, 1746, 2650, 4080, 6355, 9996, 15843, 25257, 40439, 64951, 104556, 168579, 272108, 439556, 710424, 1148626, 1857577, 3004606, 4860457, 7863203, 12721661, 20582721, 33302090, 53882365, 87181850, 141061446

Offset

1,1

Comments

Column 5 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.

Conjectures from Colin Barker, Feb 17 2018: (Start)

G.f.: x*(115 - 269*x + 68*x^2 + 193*x^3 - 118*x^4 + 6*x^5) / ((1 - x)^3*(1 - x - x^2)).

a(n) = 34 + (2^(-1-n)*((1-sqrt(5))^n*(-11+53*sqrt(5)) + (1+sqrt(5))^n*(11+53*sqrt(5)))) / sqrt(5) + 14*(1+n) + (5/2)*(1 + n)*(2+n) for n>1.

(End)

Example

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

Crossrefs

Sequence in context: A051975 A363790 A183626 * A181931 A229324 A277806

Adjacent sequences: A224670 A224671 A224672 * A224674 A224675 A224676

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved