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

0,3

Comments

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

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).

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

Example

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

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 *)

Prog

(PARI) for(n=0, 50, print1(lcm(3, n^2 + n +1)/3, ", ")) \\ G. C. Greubel, Oct 26 2017
(Magma) [Lcm(3, n^2+n+1)/3: n in [0..50]]; // G. C. Greubel, Oct 26 2017

Crossrefs

Cf. A051176, A130723.

Sequence in context: A357127 A081257 A046163 * A158622 A367866 A369717

Adjacent sequences: A130767 A130768 A130769 * A130771 A130772 A130773

Keyword

easy,nonn

Author

W. Neville Holmes, Jul 14 2007

Status

approved