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%I #15 Aug 23 2017 14:29:39
%S 1,6,7,4,6,4,7,6,1,1,6,7,4,6,4,7,6,1,1,6,7,4,6,4,7,6,1,1,6,7,4,6,4,7,
%T 6,1,1,6,7,4,6,4,7,6,1,1,6,7,4,6,4,7,6,1,1,6,7,4,6,4,7,6,1,1,6,7,4,6,
%U 4,7,6,1,1,6,7,4,6,4,7,6,1,1,6,7,4,6
%N Digital roots of centered pentagonal numbers (A005891).
%C The sequence is periodic with period 9.
%H Colin Barker, <a href="/A254374/b254374.txt">Table of n, a(n) for n = 1..1000</a>
%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(A005891(n)).
%F a(n) = a(n-9).
%F G.f.: -x*(x^8+6*x^7+7*x^6+4*x^5+6*x^4+4*x^3+7*x^2+6*x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)).
%e a(3) = 7 because the 3rd centered pentagonal number is 16, the digital root of which is 7.
%t FixedPoint[Plus @@ IntegerDigits[#] &, #] & /@ Table[(5 n^2 + 5 n + 2)/2, {n, 0, 80}] (* _Michael De Vlieger_, Feb 01 2015 *)
%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 6, 7, 4, 6, 4, 7, 6, 1},86] (* _Ray Chandler_, Aug 26 2015 *)
%t PadRight[{},120,{1,6,7,4,6,4,7,6,1}] (* _Harvey P. Dale_, Aug 23 2017 *)
%o (PARI) m=5; vector(200, n, (m*n*(n-1)/2)%9+1)
%Y Cf. A001844, A005891.
%K nonn,easy,base
%O 1,2
%A _Colin Barker_, Jan 29 2015
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