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%I #27 Dec 19 2020 07:52:32
%S 1,9,49,81,121,169,289,361,441,529,729,841,961,1089,1369,1521,1681,
%T 1849,2209,2401,2601,2809,3249,3481,3721,3969,4489,4761,5041,5329,
%U 5929,6241,6561,6889,7569,7921,8281,8649,9409,9801,10201,10609,11449,11881,12321
%N Squares of (odd numbers not divisible by 5).
%C Catalan stated empirically that the triple of any odd square not divisible by 5 is a sum of squares of three primes other than 2 and 3. - _Jonathan Vos Post_, Mar 03 2010 [Reference?]
%H Rodolfo Ruiz-Huidobro, <a href="/A028375/b028375.txt">Table of n, a(n) for n = 1..250</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).
%F a(n) = (A045572(n))^2.
%F a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9). - _R. J. Mathar_, Sep 22 2009
%F G.f.: x*(1 + 8*x + 40*x^2 + 32*x^3 + 38*x^4 + 32*x^5 + 40*x^6 + 8*x^7 + x^8)/((1 + x)^2 * (x^2 + 1)^2 * (1 - x)^3). - _R. J. Mathar_, Sep 22 2009
%F Sum_{n>=1} 1/a(n) = 3*Pi^2/25. - _Amiram Eldar_, Dec 19 2020
%t Select[Range[1, 191, 2], Mod[#, 5] != 0 &]^2 (* or *) LinearRecurrence[{1, 0, 0, 2, -2, 0, 0, -1, 1}, {1, 9, 49, 81, 121, 169, 289, 361, 441}, 50] (* _Harvey P. Dale_, Feb 26 2017 *)
%t Complement[2Range[100] - 1, 5Range[20]]^2 (* _Alonso del Arte_, Dec 23 2019 *)
%o (Scala) ((1 to 99 by 2).diff(5 to 100 by 5)).map(n => (n * n)) // _Alonso del Arte_, Dec 23 2019
%K nonn,easy
%O 1,2
%A ems (nibor(AT)ix.netcom.com)
%E Definition corrected by _R. J. Mathar_, Sep 22 2009
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