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%I #29 Sep 08 2022 08:46:21
%S -10,0,30,80,150,240,350,480,630,800,990,1200,1430,1680,1950,2240,
%T 2550,2880,3230,3600,3990,4400,4830,5280,5750,6240,6750,7280,7830,
%U 8400,8990,9600,10230,10880,11550,12240,12950,13680,14430,15200,15990,16800,17630,18480,19350,20240
%N Numbers k such that k/10 + 1 is a square.
%C Equivalently, numbers k such that (k + 10)*10 is a square.
%C The positive terms belong to the fourth column of the array in A185781.
%H Bruno Berselli, <a href="/A302576/b302576.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F O.g.f.: -10*x*(1 - 3*x)/(1 - x)^3.
%F E.g.f.: -10*x*(1 - x)*exp(x).
%F a(n) = a(2-n).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F a(n) = 10*n*(n - 2) = 10*A067998(n).
%F a(n) = A033583(n-1) - 10. - _Altug Alkan_, Apr 10 2018
%t Table[10 n (n - 2), {n, 1, 50}]
%o (PARI) vector(50, n, nn; 10*n*(n-2))
%o (Maxima) makelist(10*n*(n-2), n, 1, 50);
%o (GAP) List([1..50], n -> 10*n*(n-2));
%o (Julia) [10*n*(n-2) for n in 1:50] |> println
%o (Sage) [10*n*(n-2) for n in (1..50)]
%o (Python) [10*n*(n-2) for n in range(1, 50)]
%o (Magma) [10*n*(n-2): n in [1..50]];
%Y Cf. A000290, A008592, A033583, A185781.
%Y After -10, subsequence of A174133 because a(n) = ((n-1)^2-1)*(3^2+1).
%Y Similar lists of k for which k/j + 1 is a square: A067998 (j=1), A054000 (j=2), A067725 (j=3), A134582 (j=4), A067724 (j=5), A067726 (j=6), A067727 (j=7), second bisection of A067728 (j=8), A147651 (j=9), this sequence (j=10), A067705 (j=11), second bisection of A067707 (j=12).
%K sign,easy
%O 1,1
%A _Bruno Berselli_, Apr 10 2018
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