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

Author

Mark Richardson, Aug 21 2016

Keywords

• nonn
• easy

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

Crossrefs

Cf. A002021, A052928.

Programs

Magma

[((n-1)^(n-1 div 2 +(-1)^n div 2)-1) div n: n in [1..25]]; // Vincenzo Librandi, May 15 2019

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 *)

PARI

a(n) = ((n-1)^(n-1/2+(-1)^n/2)-1)/n \\ Felix Fröhlich, Aug 26 2016

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