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%I #29 Feb 16 2023 05:08:32
%S 4,64,144,324,484,784,1024,1444,1764,2304,2704,3364,3844,4624,5184,
%T 6084,6724,7744,8464,9604,10404,11664,12544,13924,14884,16384,17424,
%U 19044,20164,21904,23104,24964,26244,28224,29584,31684,33124,35344,36864,39204
%N Squares ending in digit 4.
%H Seiichi Manyama, <a href="/A273375/b273375.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F G.f.: 4*x*(1 + 15*x + 18*x^2 + 15*x^3 + x^4) /((1+x)^2*(1-x)^3).
%F a(n) = 4*A047209(n)^2 = (10*n + (-1)^n - 5)^2/4.
%F Sum_{n>=1} 1/a(n) = 2*Pi^2/(25*(5-sqrt(5))). - _Amiram Eldar_, Feb 16 2023
%t Table[(10 n + (-1)^n - 5)^2/4, {n, 1, 50}] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {4, 64, 144, 324, 484}, 50]
%t Select[Range[200]^2,Mod[#,10]==4&] (* or *) LinearRecurrence[{1,1,-1},{2,8,12},40]^2(* _Harvey P. Dale_, Aug 06 2017 *)
%o (Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n, 2, 10) eq 4];
%o (Magma) [(10*n+(-1)^n-5)^2/4: n in [1..50]];
%Y Cf. A000290, A047209.
%Y Cf. A017317 (numbers ending in 4), A017319 (cubes ending in 4).
%Y Cf. similar sequences listed in A273373.
%K nonn,base,easy
%O 1,1
%A _Vincenzo Librandi_, May 24 2016
%E Edited by _Bruno Berselli_, May 24 2016
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