A117794 Hexagonal numbers divisible by 6.

0, 6, 66, 120, 276, 378, 630, 780, 1128, 1326, 1770, 2016, 2556, 2850, 3486, 3828, 4560, 4950, 5778, 6216, 7140, 7626, 8646, 9180, 10296, 10878, 12090, 12720, 14028, 14706, 16110, 16836, 18336, 19110, 20706, 21528, 23220, 24090, 25878, 26796

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 29 2006

Keywords

• nonn
• easy

Comments

Intersection of A000384 and A008588. Their indices are given by A047238. - Michel Marcus, Feb 27 2014

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A000384, A008588, A047238.

Programs

Mathematica

Select[Table[n(2n-1),{n,0,250}],Divisible[#,6]&] (* or *) LinearRecurrence[ {1,2,-2,-1,1},{0,6,66,120,276},84] (* Harvey P. Dale, Aug 19 2011 *)

PARI

isok(n) = ispolygonal(n, 6) && !(n % 6); \\ Michel Marcus, Feb 27 2014

Formula

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5), with a(1)=0, a(2)=6, a(3)=66, a(4)=120, a(5)=276. - Harvey P. Dale, Aug 19 2011

a(n) = 3/2*(-1)^n(-4 n+(-1)^n*(6*n(2*n-5)+19)+5). - Harvey P. Dale, Aug 19 2011

G.f.: 6*x^2*(1+10*x+7*x^2+6*x^3)/((1-x)^3*(1+x)^2). - Harvey P. Dale, Aug 19 2011