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

1,3

Links

Table of n, a(n) for n=1..50.

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

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

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 *)

Prog

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

Crossrefs

Cf. A152018, A195055.

Sequence in context: A272033 A356356 A098289 * A055516 A248314 A174837

Adjacent sequences: A152017 A152018 A152019 * A152021 A152022 A152023

Keyword

nonn,mult

Author

Paul Curtz, Nov 20 2008

Extensions

More terms from Michel Marcus, Jun 01 2013

Keyword:mult added by Andrew Howroyd, Jul 25 2018

Status

approved