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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 (list; graph; refs; listen; history; text; internal format)
 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) = 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. Cf. A007310, A001318, A033683, A100044. Sequence in context: A109861 A106564 A308177 * A289829 A131706 A110015 Adjacent sequences:  A104774 A104775 A104776 * A104778 A104779 A104780 KEYWORD nonn AUTHOR Michael Somos, Mar 24 2005 STATUS approved

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Last modified January 20 01:46 EST 2021. Contains 340300 sequences. (Running on oeis4.)