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A104777
Integer squares congruent to 1 mod 6.
6
1, 25, 49, 121, 169, 289, 361, 529, 625, 841, 961, 1225, 1369, 1681, 1849, 2209, 2401, 2809, 3025, 3481, 3721, 4225, 4489, 5041, 5329, 5929, 6241, 6889, 7225, 7921, 8281, 9025, 9409, 10201, 10609, 11449, 11881, 12769, 13225, 14161, 14641, 15625, 16129
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
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) = A007310(n)^2 = 1 + 24*A001318(n-1).
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
Disjoint union of A016922 and A016970.
Sequence in context: A348754 A106564 A308177 * A289829 A358060 A131706
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 24 2005
STATUS
approved