OFFSET
1,2
COMMENTS
Exponents of powers of q in expansion of eta(q^24).
Odd squares not divisible by 3. - Reinhard Zumkeller, Nov 14 2015
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1)
FORMULA
A033683(a(n)) = 1.
G.f.: ( -1-24*x-22*x^2-24*x^3-x^4 ) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Feb 20 2011
a(n) = 9*n^2 - 9*n + 5/2 + (-1)^n * (3*n - 3/2). a(n+4) = 2*a(n+2) - a(n) + 72. - Robert Israel, Dec 12 2014
a(n) == 1 (mod 24). - Joerg Arndt, Jan 03 2017
Sum_{n>=1} 1/a(n) = Pi^2/9 (A100044). - Amiram Eldar, Dec 19 2020
EXAMPLE
eta(q^24) = q - q^25 - q^49 + q^121 + q^169 - q^289 - q^361 + ...
MAPLE
seq(9*(n-1/2)^2 + 1/4 + (-1)^n * (3*n - 3/2), n = 1 .. 100); # Robert Israel, Dec 12 2014
MATHEMATICA
Select[Range[130]^2, Mod[#, 6]==1&] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {1, 25, 49, 121, 169}, 50] (* Harvey P. Dale, Mar 09 2017 *)
PROG
(PARI) {a(n) = (3*n - 1 - n%2)^2};
(Haskell)
a104777 = (^ 2) . a007310 -- Reinhard Zumkeller, Nov 14 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 24 2005
STATUS
approved