A130723 Least common multiple of 3 and n^2+n+1.

3, 3, 21, 39, 21, 93, 129, 57, 219, 273, 111, 399, 471, 183, 633, 723, 273, 921, 1029, 381, 1263, 1389, 507, 1659, 1803, 651, 2109, 2271, 813, 2613, 2793, 993, 3171, 3369, 1191, 3783, 3999, 1407, 4449, 4683, 1641, 5169, 5421, 1893, 5943, 6213, 2163, 6771

Offset: 0

Author

W. Neville Holmes, Jul 04 2007

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Crossrefs

Cf. A109044.

Programs

Mathematica

Table[LCM[3,n^2+n+1],{n,0,60}] (* Harvey P. Dale, Mar 03 2017 *)

PARI

a(n) = lcm(3, n^2+n+1) \\ Michel Marcus, Jul 11 2013

PARI

Vec(3*(1 + x + 7*x^2 + 10*x^3 + 4*x^4 + 10*x^5 + 7*x^6 + x^7 + x^8) / ((1 - x)^3*(1 + x + x^2)^3) + O(x^100)) \\ Colin Barker, Mar 08 2017

Formula

From Colin Barker, Mar 08 2017: (Start)

G.f.: 3*(1 + x + 7*x^2 + 10*x^3 + 4*x^4 + 10*x^5 + 7*x^6 + x^7 + x^8) / ((1 - x)^3*(1 + x + x^2)^3).

a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>8.

(End)

Extensions

Corrected by Harvey P. Dale, Mar 03 2017