OFFSET
1,2
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
G. C. Greubel, Table of n, a(n) for n = 1..5000
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).
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
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 *)
PROG
(PARI) a(n) = denominator((n-1)*(n+1)/(9*n^2)); \\ Michel Marcus, Mar 17 2018
(Magma)
A147650:= func< n | Denominator((n^2-1)/(9*n^2)) >;
[A147650(n): n in [1..70]]; // G. C. Greubel, Dec 18 2025
(SageMath)
def A147650(n): return denominator((n-1)*(n+1)/(9*n^2))
print([A147650(n) for n in range(1, 41)]) # G. C. Greubel, Dec 18 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 09 2008
EXTENSIONS
Offset changed from 0 to 1, and extended by Wolfdieter Lang, Mar 16 2018
More terms added by G. C. Greubel, Dec 18 2025
STATUS
approved
