A260640 Numbers n such that binomial(3*n,n) == 0 (mod n).

1, 3, 6, 12, 21, 35, 44, 55, 60, 70, 78, 88, 90, 99, 102, 110, 117, 119, 120, 133, 156, 171, 176, 180, 184, 204, 207, 220, 225, 230, 231, 234, 238, 240, 247, 252, 255, 285, 286, 300, 312, 341, 342, 348, 360, 368, 372, 391, 403, 408, 414, 425, 434, 460, 462, 465, 468, 481, 483, 494, 495, 504, 506, 510, 550, 555, 561, 572, 574, 585, 600

Offset

1,2

Comments

See A014847 for the analog for 2n.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

M. Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems, sect. III: Binomial coefficients modulo integers, binomod.gp (v.1.4, 11/2015).

Mathematica

Select[Range@ 600, Mod[Binomial[3 #, #], #] == 0 &] (* Michael De Vlieger, Nov 12 2015 *)

Prog

(PARI) for(n=1, 999, binomod(3*n, n, n)==0&&print1(n", ")) \\ Using binomod.gp by M. Alekseyev, cf. links.
(Python)
from __future__ import division
A260640_list, b = [], 3
for n in range(1, 10**3):
    if not b % n:
        A260640_list.append(n)
    b = b*3*(3*n+2)*(3*n+1)//((2*n+2)*(2*n+1)) # Chai Wah Wu, Jan 27 2016
(Magma) [n: n in [1..600] |Binomial(3*n, n) mod n eq 0]; // Vincenzo Librandi, Jan 29 2016

Crossrefs

Cf. A260636, A080469, A109641, A109642, A014847.

Sequence in context: A161809 A084439 A034344 * A203292 A054578 A115855

Adjacent sequences: A260637 A260638 A260639 * A260641 A260642 A260643

Keyword

nonn

Author

M. F. Hasler, Nov 11 2015

Status

approved