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A273374 Squares ending in digit 9.

%I A273374 #39 Mar 09 2023 02:21:51
%S A273374 9,49,169,289,529,729,1089,1369,1849,2209,2809,3249,3969,4489,5329,
%T A273374 5929,6889,7569,8649,9409,10609,11449,12769,13689,15129,16129,17689,
%U A273374 18769,20449,21609,23409,24649,26569,27889,29929,31329,33489,34969,37249,38809
%N A273374 Squares ending in digit 9.
%C A273374 A quasipolynomial of order two and degree two: a(n) = 25n^2 - 30n + 9 if n is even and 25n^2 - 20n + 4 if n is odd. - _Charles R Greathouse IV_, Nov 03 2021
%H A273374 Seiichi Manyama, <a href="/A273374/b273374.txt">Table of n, a(n) for n = 1..10000</a>
%H A273374 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A273374 G.f.: x*(9 + 40*x + 102*x^2 + 40*x^3 + 9*x^4)/((1 + x)^2*(1 - x)^3).
%F A273374 a(n) = 6 + (50*(n-1)*n - 5*(2*n-1)*(-1)^n + 1)/2.
%F A273374 a(n) = A063226(n)^2. - _Seiichi Manyama_, May 25 2016
%F A273374 Sum_{n>=1} 1/a(n) = Pi^2*(3-sqrt(5))/50. - _Amiram Eldar_, Feb 16 2023
%t A273374 Table[6 + (50 (n - 1) n - 5 (2 n - 1) (-1)^n + 1)/2, {n, 1, 50}]
%o A273374 (Magma) /* By definition: */ [n^2: n in [0..200] | Modexp(n,2,10) eq 9];
%o A273374 (Magma) [6+(50*(n-1)*n-5*(2*n-1)*(-1)^n+1)/2: n in [1..50]];
%o A273374 (PARI) a(n)=(5*n-3+n%2)^2 \\ _Charles R Greathouse IV_, Nov 03 2021
%Y A273374 Cf. A000290, A016754, A063226.
%Y A273374 Cf. A017377 (numbers ending in 9), A017379 (cubes ending in 9).
%Y A273374 Cf. similar sequences listed in A273373.
%K A273374 nonn,base,easy
%O A273374 1,1
%A A273374 _Vincenzo Librandi_, May 21 2016
%E A273374 Corrected and extended by _Bruno Berselli_, May 21 2016