%I #24 Mar 22 2022 18:34:16
%S 2,11,106,1277,18746,326587,6588338,150994937,3874204882,109999999991,
%T 3423740047322,115909305827317,4240251492291530,166680102383370227,
%U 7006302246093749986,313594649253062377457,14890324713954061755170,747581753430634213933039,39568393113206271782479562
%N a(n) = (n+1)*n^n + n - 1.
%C Arises in studying the "Pile of pairs of coconuts (and pals)" problem.
%C Motivated by a question passed along by Timothy Hunt from Kara Goeke; it is a generalization of the exercise in the first reference, which asks for a solution for n=3. For odd-indexed terms, the index may be taken as the number of participants in the circle. (The game doesn't work for even numbers of participants.)
%C In the case in the exercise: there are three participants splitting a box of chocolates whose number is even. The first person takes one, notes that the remainder is divisible by three, takes 1/3 of the remaining chocolates, passes the remainder to the second person, who takes one, notes that the remainder is divisible by three, takes 1/3 of the remaining chocolates, and passes the remainder to the last person, who takes one, notes that the remainder is divisible by three, and takes 1/3 of the remainder. The number of chocolates remaining after this last division are once again divisible by three.
%C The generalization that this sequence solves is that there are any odd number of people n in the circle, and that they each take 1/n of the remainder after taking their initial single item; the final number left is divisible by n as well.
%C The "Pals" part is that although this only represents solutions to the problem for an odd number of participants, the formula that generates those solutions is perfectly well-behaved for even n as well, and those may as well be terms in the sequence.
%C This is the same basic problem as A002021, with the further constraint that the initial number of coconuts be even.
%D Mark Dugopolski, College Algebra, Addison-Wesley, 1995, page 16, exercise 123.
%Y Cf. A002021.
%K nonn,easy
%O 1,1
%A _Adam Thornton_, Feb 07 2022
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