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) + -1a(n + -3)

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

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

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

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

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

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

Combine like terms: -3a + 3a = 0
an = 0 + an + an + -1an
an = an + an + -1an

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

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

Solving
an = 1an

Solving for variable 'a'.

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

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

Combine like terms: an + -1an = 0
0 = 1an + -1an

Combine like terms: 1an + -1an = 0
0 = 0

Simplifying
0 = 0

The solution to this equation could not be determined.