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%I #21 Jan 24 2020 05:34:28
%S 1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,
%T 8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,
%U 5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8,8,1,5,2,1
%N Digital root of n + (n+1)^2.
%C Period 9: repeat [1,5,2,1,2,5,1,8,8].
%C When expressed starting from the 9th term, i.e., 8,1,5,2,1,2,5,1,8,8,1,5,2,1,2,5,1,8, etc., the sequence is palindromic.
%C Decimal expansion is 50708396/333333333.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F a(n) = A010888(A028387(n)).
%F G.f.: ( -1 - 5*x - 2*x^2 - x^3 - 2*x^4 - 5*x^5 - x^6 - 8*x^7 - 8*x^8 ) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). - _R. J. Mathar_, Jan 07 2019
%t Table[FixedPoint[Total@ IntegerDigits@ # &, n + (n + 1)^2], {n, 0, 120}] (* or *)
%t PadRight[{}, 120, {1, 5, 2, 1, 2, 5, 1, 8, 8}] (* _Michael De Vlieger_, Aug 07 2016 *)
%Y Cf. A010888, A028387.
%K nonn,easy,base
%O 0,2
%A _Peter M. Chema_, Aug 05 2016
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