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%I #13 Aug 26 2015 17:14:03
%S 1,8,4,7,8,7,4,8,1,1,8,4,7,8,7,4,8,1,1,8,4,7,8,7,4,8,1,1,8,4,7,8,7,4,
%T 8,1,1,8,4,7,8,7,4,8,1,1,8,4,7,8,7,4,8,1,1,8,4,7,8,7,4,8,1,1,8,4,7,8,
%U 7,4,8,1,1,8,4,7,8,7,4,8,1,1,8,4,7,8
%N Digital roots of centered heptagonal numbers (A069099).
%C The sequence is periodic with period 9.
%H Colin Barker, <a href="/A254375/b254375.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(A069099(n)).
%F a(n) = a(n-9).
%F G.f.: -x*(x^8+8*x^7+4*x^6+7*x^5+8*x^4+7*x^3+4*x^2+8*x+1) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)).
%e a(3) = 4 because the 3rd centered heptagonal number is 22, the digital root of which is 4.
%t FixedPoint[Plus @@ IntegerDigits[#] &, #] & /@ FoldList[#1 + #2 &, 1, 7 Range@ 80] (* _Michael De Vlieger_, Feb 01 2015, after _Robert G. Wilson v_ at A069099 *)
%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1},{1, 8, 4, 7, 8, 7, 4, 8, 1},86] (* _Ray Chandler_, Aug 26 2015 *)
%o (PARI) m=9; vector(200, n, (m*n*(n-1)/2)%9+1)
%Y Cf. A001844, A069099.
%K nonn,easy,base
%O 1,2
%A _Colin Barker_, Jan 29 2015
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