Padovan numbers which are concatenations of three repdigits

On a Generalization of the Padovan Numbers

“…The Padovan sequence [1,2] is the integer sequence P(n) defined by the recurrence relation P(n) = P(n-2) + P(n-3) with initial values P(0) = P(1) = P(2) = 1.…”

“…Galois theory allows proving that when the three roots are real, and none is rational (casus irreducibilis), one cannot express the roots in terms of real radicals. Nevertheless, purely real expressions of the solutions may be obtained using trigonometric functions, specifically in terms of cosines [1].…”