A175676 a(n) = binomial(n,3) mod n.

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

Author

Zak Seidov, Aug 07 2010

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A007290.

Programs

GAP

List([1..100],n->Binomial(n,3) mod n); # Muniru A Asiru, Apr 05 2018

Mathematica

Table[Mod[Binomial[n,3],n],{n,150}]

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

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