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A224673 Number of (n+1) X 6 0..2 matrices with each 2 X 2 subblock idempotent 1
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 (list; graph; refs; listen; history; text; internal format)
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: A095621 A051975 A183626 * A181931 A229324 A277806

Adjacent sequences:  A224670 A224671 A224672 * A224674 A224675 A224676

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 14 2013

STATUS

approved

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Last modified September 27 02:43 EDT 2021. Contains 347673 sequences. (Running on oeis4.)