A351331 a(n) = (n+1)*(n^n) - n + 1.

2, 11, 106, 1277, 18746, 326587, 6588338, 150994937, 3874204882, 109999999991, 3423740047322, 115909305827317, 4240251492291530, 166680102383370227, 7006302246093749986, 313594649253062377457, 14890324713954061755170, 747581753430634213933039, 39568393113206271782479562

Offset

1,1

Comments

Arises in studying the "Pile of pairs of coconuts (and pals)" problem.

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.)

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.

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.

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.

This is the same basic problem as A002021, with the further constraint that the initial number of coconuts be even.

References

Mark Dugopolski, College Algebra, Addison-Wesley, 1995, page 16, exercise 123.

Links

Table of n, a(n) for n=1..19.

Maple

seq((n+1)*(n^n)-n+1, n=1..19); # Georg Fischer, Apr 10 2024

Crossrefs

Cf. A002021.

Sequence in context: A268294 A364338 A207571 * A278070 A292428 A088690

Adjacent sequences: A351328 A351329 A351330 * A351332 A351333 A351334

Keyword

nonn,easy

Author

Adam Thornton, Feb 07 2022

Extensions

Definition corrected by Georg Fischer, Apr 10 2024

Status

approved