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A175676
a(n) = binomial(n,3) mod n.
10
0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, 0, 0, 6, 0, 0, 7, 0, 0, 8, 0, 0, 9, 0, 0, 10, 0, 0, 11, 0, 0, 12, 0, 0, 13, 0, 0, 14, 0, 0, 15, 0, 0, 16, 0, 0, 17, 0, 0, 18, 0, 0, 19, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 24, 0, 0, 25, 0, 0, 26, 0, 0, 27, 0, 0, 28, 0, 0, 29, 0, 0, 30, 0, 0, 31, 0
OFFSET
1,6
COMMENTS
Number of partitions of n+3 into 3 parts that are in arithmetic progression. - Wesley Ivan Hurt, Dec 07 2020
FORMULA
a(n) = n/3 if n==0 (mod 3) else a(n) = 0.
G.f.: x^3 / ( (x-1)^2*(1+x+x^2)^2 ). - R. J. Mathar, Mar 11 2011
a(n) = A008620(n-1)*A079978(n). - Bruno Berselli, Jun 22 2012
a(n) = (n + 2*n*cos((2*n*Pi)/3))/9. - Kritsada Moomuang, Apr 02 2018
MATHEMATICA
Table[Mod[Binomial[n, 3], n], {n, 150}]
PROG
(PARI) a(n)=if(n%3, 0, n/3); \\ Charles R Greathouse IV, Sep 02 2015 [Corrected by Altug Alkan, Apr 02 2018]
(PARI) a(n)=!(n%3)*(1-n)\-3; \\ Altug Alkan, Apr 02 2018
(GAP) List([1..100], n->Binomial(n, 3) mod n); # Muniru A Asiru, Apr 05 2018
CROSSREFS
Cf. A007290.
Sequence in context: A348127 A233440 A280728 * A035377 A136274 A290976
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Aug 07 2010
STATUS
approved