

A165987


a(n) is the trace of the matrix f(X + n*f(X))/f(X), where X is the 2 X 2 matrix [13, 17; 31, 97] and f(x) = x^3  5*x + 67.


0



1099258818702, 8792791182238, 29674231047422, 70337212371066, 137375369109982, 237382335220982, 376951744660878, 562677231386482, 801152429354606, 1098970972522062, 1462726494845662, 1899012630282218, 2414423012788542, 3015551276321446, 3708991054837742
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Old name was: As mentioned in the short description (cf. A165806 & A165808) polynomials have the property: f(x + k*f(x)) is congruent to 0 mod(f(x)). This is true even if the variable is a square matrix. For this sequence let X be a 2x2 matrix (X belongs to Z): col1:13, 31;col2: 17, 97. Let the polynomial be X^3 5X + 67. The present sequence is a sequence of traces of the matrices resulting from the division of f(X + k*f(X))/f(X). Here k belongs to N.


LINKS



FORMULA

G.f.: 2*(549309615337*x^3+2197877953721*x^2+549629409347*x+1)/(x1)^4.  Alois P. Heinz, Mar 13 2024


MAPLE

with(LinearAlgebra):
f:= x> x^35*x+67:
a:= n> (X> Trace(f(X+n*f(X)).f(X)^(1)))(<<1317>, <3197>>):


CROSSREFS



KEYWORD

nonn,easy,less


AUTHOR



EXTENSIONS



STATUS

approved



