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A137401 a(n) is the number of ordered solutions (x,y,z) to x^3 + y^3 == z^3 mod n with 1 <= x,y,z <= n-1. 2
0, 0, 2, 7, 12, 20, 0, 63, 116, 72, 90, 131, 0, 108, 182, 339, 240, 602, 324, 415, 326, 420, 462, 839, 604, 216, 1808, 763, 756, 812, 810, 1735, 992, 1056, 1092, 3311, 648, 1620, 650, 2511, 1560, 1640, 1134, 2227, 4328, 1980, 2070, 3683, 2484, 2644, 2450, 1519 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Record values of A137401: 0, 2, 7, 12, 20, 63, 116, 131, 182, 339, 602, 839, 1808, 3311, 4328, 7964, 8864, 9231, 19583, 21986, 41363, 52676, 81467, 87596, 92087, 112616, 236951, 247940, 378071, 386423, 521135, ... - Robert G. Wilson v

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..425 from Robert G. Wilson v)

FORMULA

a(n) = A063454(n)-3*A087786(n)+3*A000189(n)-1. - Vladeta Jovovic, Apr 11 2008

EXAMPLE

a(4)=7 because (1, 2, 1), (1, 3, 2), (2, 1, 1), (2, 2, 2), (2, 3, 3), (3, 1, 2), (3, 2, 3) are solutions for n=4.

MATHEMATICA

f[n_] := Block[ {c = 0}, Do[ If[ Mod[x^3 + y^3, n] == Mod[z^3, n], c++ ], {x, n - 1}, {y, n - 1}, {z, n - 1}]; c];

Table[Length[Select[Tuples[Range[n - 1], 3], Mod[ #[[1]]^3 + #[[2]]^3 - #[[3]]^3, n] == 0 &]], {n, 2, 50}] (* Stefan Steinerberger, Apr 12 2008 *)

PROG

(Python)

def A137401(n):

    ndict = {}

    for i in range(1, n):

        m = pow(i, 3, n)

        if m in ndict:

            ndict[m] += 1

        else:

            ndict[m] = 1

    count = 0

    for i in ndict:

        ni = ndict[i]

        for j in ndict:

            k = (i+j) % n

            if k in ndict:

                count += ni*ndict[j]*ndict[k]

    return count # Chai Wah Wu, Jun 06 2017

CROSSREFS

Cf. A063454.

Sequence in context: A188039 A133459 A023669 * A309150 A333354 A119713

Adjacent sequences:  A137398 A137399 A137400 * A137402 A137403 A137404

KEYWORD

nonn

AUTHOR

Neven Juric (neven.juric(AT)apis-it.hr), Apr 11 2008

EXTENSIONS

More terms from Stefan Steinerberger and Robert G. Wilson v, Apr 12 2008

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)