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A173500 Number of sequences of length n with terms from {0,1,...,n-1} such that the sum of terms is 0 modulo n and the i-th term is not i or 2i modulo n. 2
0, 0, 0, 6, 64, 854, 13392, 244944, 5124266, 120795956, 3169804000, 91666666668, 2897010809280, 99350833566282, 3674884626652666, 145845089585448960, 6182031393612132352, 278750799336055446646, 13322922112485213149376 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Robert Israel, Table of n, a(n) for n = 1..200

Art of Problem Solving forum, 45th IMO Team Selection Test Lincoln, Nebraska.

FORMULA

For prime p, a(p) = (p-1)*((p-2)^(p-1)-1)/p.

EXAMPLE

For n=4 the a(4)=6 sequences are 0103, 0112, 0301, 3113, 3302 and 3311. - Robert Israel, Aug 30 2020

MAPLE

f:= proc(n)

local g;

  g:= proc(i, s) option remember;

    if i = 0 then if s=0 then return 1 else return 0 fi fi;

    add(procname(i-1, s-k mod n), k= {$0..n-1} minus {2*i mod n, i})

  end proc;

  g(n, 0)

end proc:

map(f, [$1..30]); # Robert Israel, Aug 30 2020

CROSSREFS

Cf. A173499.

Sequence in context: A239847 A264634 A296165 * A141008 A336114 A258425

Adjacent sequences:  A173497 A173498 A173499 * A173501 A173502 A173503

KEYWORD

nonn

AUTHOR

Max Alekseyev, Feb 20 2010

STATUS

approved

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Last modified September 17 18:22 EDT 2021. Contains 347489 sequences. (Running on oeis4.)