A152020 Denominator of 8/(9n^2) divided by 9.

1, 1, 9, 2, 25, 9, 49, 8, 81, 25, 121, 18, 169, 49, 225, 32, 289, 81, 361, 50, 441, 121, 529, 72, 625, 169, 729, 98, 841, 225, 961, 128, 1089, 289, 1225, 162, 1369, 361, 1521, 200, 1681, 441, 1849, 242, 2025, 529, 2209, 288, 2401, 625

Offset: 1

Author

Paul Curtz, Nov 20 2008

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A152018, A195055.

Programs

Mathematica

Denominator[8/(9*Range[50]^2)]/9 (* or *) LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {1, 1, 9, 2, 25, 9, 49, 8, 81,  25, 121, 18}, 50] (* Harvey P. Dale, Aug 25 2013 *)

PARI

a(n) = denominator(8/(9*n^2))/9 \\ Michel Marcus, Jun 01 2013

Formula

a(n) = A152018(n)/9.

a(1)=1, a(2)=1, a(3)=9, a(4)=2, a(5)=25, a(6)=9, a(7)=49, a(8)=8, a(9)=81, a(10)=25, a(11)=121, a(12)=18, a(n)=3*a(n-4)-3*a(n-8)+a(n-12). - Harvey P. Dale, Aug 25 2013

Conjecture: a(n) = denominator((n-2)^3/n^2). - Andres Cicuttin, Sep 19 2017

a(n) = n^2/gcd(n^2, 8). - Andrew Howroyd, Jul 25 2018

Sum_{n>=1} 1/a(n) = Pi^2/3 (A195055). - Amiram Eldar, Sep 14 2022

Extensions

More terms from Michel Marcus, Jun 01 2013

Keyword:mult added by Andrew Howroyd, Jul 25 2018