Express 3x4+2x3 - 2x2+x in terms of [x]4, [x]3, [x]2 and [x].
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Write (x z)
(y
z') in CNF and DNF.
Solve the recurrence
6an+3-13an+2+9an+1-2an = 2-n;n > 0; if a0 = 1;a1 = 1;a2 = 1
Find the general form of the solution to a linear homogeneous recurrence with constant coefficients for which the characteristic roots are 1 with multiplicity 1, -2 with multiplicity 2 and 2 with multiplicity 3. The relation also has a non-homogeneous part which is a linear combination of n2n and (-2)n
Find the generating function of the recurrence
an = 4an-1-4an-2+1
with initial conditions a0 = 1, a1 = 1.
Show that any tree with exactly two vertices of degree 1 is a path.
Express 3x4+2x3 - 2x2+x in terms of [x]4, [x]3, [x]2 and [x].
Give the order and the degree of the recurrence
a2 n+2 = a2n +2an+4
Is the recurrence homogeneous?