A130770 One third of the least common multiple of 3 and n^2+n+1.

1, 1, 7, 13, 7, 31, 43, 19, 73, 91, 37, 133, 157, 61, 211, 241, 91, 307, 343, 127, 421, 463, 169, 553, 601, 217, 703, 757, 271, 871, 931, 331, 1057, 1123, 397, 1261, 1333, 469, 1483, 1561, 547, 1723, 1807, 631, 1981, 2071, 721, 2257, 2353, 817, 2551, 2653, 919

Offset: 0

Author

W. Neville Holmes, Jul 14 2007

Keywords

• easy
• nonn

Comments

This is a subset of A051176 and is also one third of A130723.

Examples

			a(4)=7 because 4^2+4+1 =21, the LCM of 3 and 21 is 21 and 21/3=7.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 3, 0, 0, -3, 0, 0, 1).

Crossrefs

Cf. A051176, A130723.

Programs

Magma

[Lcm(3,n^2+n+1)/3: n in [0..50]]; // G. C. Greubel, Oct 26 2017

Maple

seq(denom((n-1)^2/(n^2+n+1)), n=0..52) ; # Zerinvary Lajos, Jun 04 2008

Mathematica

Table[LCM[3,n^2+n+1]/3,{n,0,60}] (* or *) LinearRecurrence[ {0,0,3,0,0,-3,0,0,1},{1,1,7,13,7,31,43,19,73},60] (* Harvey P. Dale, Apr 10 2014 *)

PARI

for(n=0,50, print1(lcm(3, n^2 + n +1)/3, ", ")) \\ G. C. Greubel, Oct 26 2017

Formula

Conjecture: a(n) = A046163(n), n>0. - R. J. Mathar, Jun 13 2008

a(n) = 3*a(n-3)-3*a(n-6)+a(n-9), with a(0)=1, a(1)=1, a(2)=7, a(3)=13, a(4)=7, a(5)=31, a(6)=43, a(7)=19, a(8)=73. - Harvey P. Dale, Apr 10 2014