A276135 Ben Ames Williams's Monkey and Coconuts Problem.

0, 0, 1, 20, 51, 2604, 6665, 720600, 1864135, 348678440, 909090909, 261535698060, 685853880635, 281241170407092, 740800455037201, 410525522232055664, 1085102592571150095, 781282469559318055056, 2070863582910344082917, 1879498672877297909667780, 4993219047619047619047619, 5577014881186619679500164220

Offset

1,4

Comments

In Ben Ames Williams's coconuts problem, a pile of coconuts remains the next day that is divisible by n sailors. Integers in the sequence multiplied by (n^2)-n determine the size of the divisible pile.

Links

Mark Richardson, Table of n, a(n) for n = 1..101

M. B. Richardson, A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Coconuts Problem, The Winnower, 3 (2016), e147175.52128. doi: 10.15200/winn.147175.52128

Formula

a(n) = ((n-1)^(n-1) - 1)/n, if n is odd.

a(n) = ((n-1)^n - 1)/n, if n is even.

a(n) = ((n-1)^(n - 1/2 + (-1)^n/2) - 1)/n = (n^A052928(n) - 1)/n. - Omar E. Pol, Aug 24 2016

Maple

seq(((n-1)^(n-1/2+(-1)^n/2)-1)/n, n=1..30); # Robert Israel, Aug 26 2016

Mathematica

Join[{0}, Table[((n - 1)^(n - 1/2 + (-1)^n/2) - 1)/n, {n, 2, 30}]] (* Bruno Berselli, Aug 26 2016 *)

Prog

(PARI) a(n) = ((n-1)^(n-1/2+(-1)^n/2)-1)/n \\ Felix Fröhlich, Aug 26 2016
(Magma) [((n-1)^(n-1 div 2 +(-1)^n div 2)-1) div n: n in [1..25]]; // Vincenzo Librandi, May 15 2019

Crossrefs

Cf. A002021, A052928.

Sequence in context: A049390 A220040 A128905 * A350115 A211143 A183047

Adjacent sequences: A276132 A276133 A276134 * A276136 A276137 A276138

Keyword

nonn,easy

Author

Mark Richardson, Aug 21 2016

Status

approved