a(n)=a(n-1)+a(n-3)

Solution for a(n)=a(n-1)+a(n-3) equation:

Simplifying
a(n) = a(n + -1) + a(n + -3)

Multiply a * n
an = a(n + -1) + a(n + -3)

Reorder the terms:
an = a(-1 + n) + a(n + -3)
an = (-1 * a + n * a) + a(n + -3)
an = (-1a + an) + a(n + -3)

Reorder the terms:
an = -1a + an + a(-3 + n)
an = -1a + an + (-3 * a + n * a)
an = -1a + an + (-3a + an)

Reorder the terms:
an = -1a + -3a + an + an

Combine like terms: -1a + -3a = -4a
an = -4a + an + an

Combine like terms: an + an = 2an
an = -4a + 2an

Solving
an = -4a + 2an

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '4a' to each side of the equation.
4a + an = -4a + 4a + 2an

Combine like terms: -4a + 4a = 0
4a + an = 0 + 2an
4a + an = 2an

Add '-2an' to each side of the equation.
4a + an + -2an = 2an + -2an

Combine like terms: an + -2an = -1an
4a + -1an = 2an + -2an

Combine like terms: 2an + -2an = 0
4a + -1an = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(4 + -1n) = 0

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

Move all terms containing a to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Add 'n' to each side of the equation.
-1n + n = -4 + n

Combine like terms: -1n + n = 0
0 = -4 + n

Simplifying
0 = -4 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}