Recurrence Definition and 257 Threads

  1. P

    Solving Linear Recurrence: ax_k+1 + bx_k + c

    Consider the recurrence x_k+2 = ax_k+1 + bx_k + c where c may not be zero. If a + b is not equal to 1 show that p can be found such that, if we set y_k = x_k + p, then y_k+2 = ay_k+1 + by_k. [Hence, the sequence x_k can be found provided y_k can be found] First of all, sorry about the...
  2. P

    Polynomial recurrence equation

    For our combinatorics class there is a bonus excercise in which we have to solve the following recurrence relation: L_k(x) = L_{k-1}(x) + xL_{k-2}(x) My first thought was to construct the following generating function: F(x,y) = \sum_{k=0}^{\infty} L_k(x) y^k. By putting in the...
  3. S

    Counting Towers: Finding a Recurrence Relation

    A set of blocks contains blocks of heights 1, 2, and 4 inches. Imagine constructing towers of piling block of different heights directly on top of one another. Let t(n) be the number of ways to construct a tower of height n inches. Find a recurrence relation for t(1), t(2), t(3)... Here's...
  4. N

    Recurrence relations and sequences

    Hi... 1. so can i say that a recurrence relation is a description of the operation(s) involved in a sequence...?... 2. is the formula for an arithmetic sequence, a recurrence relation...?... and is the formula for a geometric sequence, a recurrence relation...?...
  5. E

    2. Order Linear Inhomogenous Recurrence Relations with Constant Coefficients

    I need to show that the solution of a_n = c_1a_{n-1} + c_2a_{n-2} + f(n) (1) is of the form U_n = V_n + g(n) (2) where V_n is the solution of a 2. order linear homogenous recurrence relation with constant coefficients. Could I use the argument that if (2) is a solution...
  6. S

    Jong: "Eternal Recurrence Theory: Debunking the Infinite Universe Hypothesis

    Lectori salutem. Can anyone refute the finite space/energy/matter in infinite time theory? Finite space/energy/matter implies that the universe is not something endlessly extended, but set in a definite space as a definite force. Infinite time implies that it has never begun to become...
  7. S

    Exploring Eternal Recurrence: A Cosmological Inquiry

    Lectori salutem. This seems like a cosmological question, so I will put it here: Can anyone refute the finite space/energy/matter in infinite time theory? Thanks in advance. Sauw
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