RSolve

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RSolve[eqn, a[n], n]

solves a recurrence equation for the function a[n].

Solve a difference equation:

• • RSolve[a[n] == a[n+1], a[n], n]

No boundary conditions gives two general parameters:

• • RSolve[{a[n + 2] == a[n]}, a, n]

Include one boundary condition:

• • RSolve[{a[n + 2] == a[n], a[0] == 1}, a, n]

Get a “pure function” solution for a with two boundary conditions:

• • RSolve[{a[n + 2] == a[n], a[0] == 1, a[1] == 4}, a, n]