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A175676 a(n) = binomial(n,3) mod n. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Number of partitions of n+3 into 3 parts that are in arithmetic progression. - Wesley Ivan Hurt, Dec 07 2020

LINKS

Altug Alkan, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

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: A210951 A233440 A280728 * A035377 A136274 A290976

Adjacent sequences:  A175673 A175674 A175675 * A175677 A175678 A175679

KEYWORD

nonn,easy

AUTHOR

Zak Seidov, Aug 07 2010

STATUS

approved

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Last modified May 9 07:57 EDT 2021. Contains 343693 sequences. (Running on oeis4.)