A147650 First trisection of A061040.

1, 12, 81, 48, 75, 324, 147, 64, 729, 100, 363, 1296, 507, 588, 2025, 768, 289, 2916, 361, 1200, 3969, 1452, 1587, 5184, 1875, 676, 6561, 784, 2523, 8100, 2883, 3072, 9801, 3468, 1225, 11664, 1369, 4332, 13689, 4800, 5043

Offset: 1

Author

Paul Curtz, Nov 09 2008

Keywords

• nonn
• easy

Comments

a(n) gives the denominator of (n-1)*(n+1)/(9*n^2), for n >= 1. The numerator is given by A144454(n). - Wolfdieter Lang, Mar 16 2018

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A061040, A017198 (2nd trisection), A017234 (3d trisection).

Programs

Mathematica

Table[Which[MemberQ[{1, 8}, Mod[n, 9]], n^2, Mod[n, 3] != 0, 3 n^2, True, 9 n^2], {n, 41}] (* Michael De Vlieger, Mar 16 2018 *)

PARI

a(n) = denominator((n-1)*(n+1)/(9*n^2)); \\ Michel Marcus, Mar 17 2018

Formula

For n >= 1: a(n) = n^2 if n == 1 (mod 9) or == 8 (mod 9). For other n: a(n) = 3*n^2 if n == 1 (mod 3) or == 2 (mod 3), and a(n) = 9*n^2 if n == 0 (mod 3). From the denominator comment above. - Wolfdieter Lang, Mar 16 2018

Extensions

Offset changed from 0 to 1, and extended by Wolfdieter Lang, Mar 16 2018