a(n)=a(n-1)+a(n-2)+a(n-3)

Solution for a(n)=a(n-1)+a(n-2)+a(n-3) equation:

Simplifying
a(n) = a(n + -1) + a(n + -2) + a(n + -3)

Multiply a * n
an = a(n + -1) + a(n + -2) + a(n + -3)

Reorder the terms:
an = a(-1 + n) + a(n + -2) + a(n + -3)
an = (-1 * a + n * a) + a(n + -2) + a(n + -3)
an = (-1a + an) + a(n + -2) + a(n + -3)

Reorder the terms:
an = -1a + an + a(-2 + n) + a(n + -3)
an = -1a + an + (-2 * a + n * a) + a(n + -3)
an = -1a + an + (-2a + an) + a(n + -3)

Reorder the terms:
an = -1a + an + -2a + an + a(-3 + n)
an = -1a + an + -2a + an + (-3 * a + n * a)
an = -1a + an + -2a + an + (-3a + an)

Reorder the terms:
an = -1a + -2a + -3a + an + an + an

Combine like terms: -1a + -2a = -3a
an = -3a + -3a + an + an + an

Combine like terms: -3a + -3a = -6a
an = -6a + an + an + an

Combine like terms: an + an = 2an
an = -6a + 2an + an

Combine like terms: 2an + an = 3an
an = -6a + 3an

Solving
an = -6a + 3an

Solving for variable 'a'.

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

Add '6a' to each side of the equation.
6a + an = -6a + 6a + 3an

Combine like terms: -6a + 6a = 0
6a + an = 0 + 3an
6a + an = 3an

Add '-3an' to each side of the equation.
6a + an + -3an = 3an + -3an

Combine like terms: an + -3an = -2an
6a + -2an = 3an + -3an

Combine like terms: 3an + -3an = 0
6a + -2an = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(3 + -1n) = 0

Ignore the factor 2.
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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Add 'n' to each side of the equation.
-1n + n = -3 + n

Combine like terms: -1n + n = 0
0 = -3 + n

Simplifying
0 = -3 + 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}