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%I #11 Sep 08 2022 08:46:11
%S 1,3,7,4,3,4,7,3,1,1,3,7,4,3,4,7,3,1,1,3,7,4,3,4,7,3,1,1,3,7,4,3,4,7,
%T 3,1,1,3,7,4,3,4,7,3,1,1,3,7,4,3,4,7,3,1,1,3,7,4,3,4,7,3,1,1,3,7,4,3,
%U 4,7,3,1,1,3,7,4,3,4,7,3,1,1,3,7,4,3
%N Digital roots of centered 11-gonal numbers (A069125).
%C The sequence is periodic with period 9.
%H Colin Barker, <a href="/A256676/b256676.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(A069125(n)).
%F a(n) = a(n-9).
%F G.f.: -x*(x^8+3*x^7+7*x^6+4*x^5+3*x^4+4*x^3+7*x^2+3*x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)).
%e a(3) = 7 because the 3rd centered 11-gonal number is 34, the digital root of which is 7.
%t PadRight[{}, 100, {1, 3, 7, 4, 3, 4, 7, 3, 1}] (* _Vincenzo Librandi_, Apr 08 2015 *)
%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 3, 7, 4, 3, 4, 7, 3, 1},86] (* _Ray Chandler_, Aug 26 2015 *)
%o (PARI) m=11; vector(200, n, (m*n*(n-1)/2)%9+1)
%o (Magma) &cat[[1,3,7,4,3,4,7,3,1]: n in [0..10] ]; // _Vincenzo Librandi_, Apr 08 2015
%Y Cf. A010888, A069125.
%K nonn,base,easy
%O 1,2
%A _Colin Barker_, Apr 07 2015
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