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A127182 Number of distinct characteristic polynomials of n X n real robust {0,1}-matrices. 4
1, 2, 12, 156, 5612 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

a(2)=2 because there are 4 binary robust 2 X 2 matrices, but only two distinct characteristic polynomials, namely y^2-y-1 and y^2-2y+1.

a(3)=12 because there are 12 different characteristic polynomials: -1-3y-y^2+y^3, 1-2y-y^2+y^3, 1+y-3y^2+y^3, -2+3y-3y^2+y^3, -1-2y-y^2+y^3, -1-y-y^2+y^3, -1+y-2y^2+y^3, 2-y-2y^2+y^3, -1+2y-3y^2+y^3, 1-y-2y^2+y^3, 1- 2y^2+y^3, -1+3y-3y^2+y^3.

MATHEMATICA

mats[1] = {{{1}}}; mats[n_Integer?Positive] := mats[n] = Module[{newrows = Rest[Tuples[{0, 1}, {n}]], mp1 = Flatten[Function[k, Thread[(Append[ #1, #2]&)[ #1, k]]& /@ mats[n - 1]] /@ Tuples[{0, 1}, {n - 1}], 1]}, Flatten[MapThread[Function[{m, nl}, Append[m, # ]& /@ nl], {mp1, Pick[newrows, # =!= 0& /@ # ]& /@ (First /@ Dot[NullSpace /@ mp1, Transpose[newrows]])}], 1]] A127182[n_]=Length[Union[CharacteristicPolynomial[mats[n]]]]

CROSSREFS

Cf. A125587, A125593, A127183, A127184, A127186.

Sequence in context: A216351 A130529 A075631 * A326222 A330552 A208577

Adjacent sequences:  A127179 A127180 A127181 * A127183 A127184 A127185

KEYWORD

nonn

AUTHOR

Artur Jasinski and Peter Pein (petsie(AT)dordos.net), Jan 07 2007

STATUS

approved

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Last modified March 28 11:00 EDT 2020. Contains 333083 sequences. (Running on oeis4.)