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%I A133879 #13 Jul 28 2024 03:43:29
%S A133879 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,
%T A133879 4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,
%U A133879 8,8,8,8,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3
%N A133879 n modulo 9 repeated 9 times.
%C A133879 Periodic with length 9^2=81.
%H A133879 <a href="/index/Rec#order_73">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1).
%F A133879 a(n)=(1+floor(n/9)) mod 9.
%F A133879 a(n)=1+floor(n/9)-9*floor((n+9)/81).
%F A133879 a(n)=(((n+9) mod 81)-(n mod 9))/9.
%F A133879 a(n)=((n+9-(n mod 9))/9) mod 9.
%F A133879 G.f. g(x)=(1-x^9)(1+2x^9+3x^18+4x^27+5x^36+6x^45+7x^56+8x^63)/((1-x)(1-x^81)).
%F A133879 G.f. g(x)=(1-x^9)*sum{0<=k<8, (k+1)*x^(9*k)}/((1-x)(1-x^81)).
%F A133879 G.f. g(x)=(8x^81-9x^72+1)/((1-x)(1-x^9)(1-x^81)).
%t A133879 Rest[Flatten[Table[Table[Table[n,{9}],{n,0,8}],{3}],1]]//Flatten (* _Harvey P. Dale_, Apr 15 2018 *)
%Y A133879 Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.
%Y A133879 Cf. A133889, A133880, A133890, A133900, A133910.
%K A133879 nonn,easy
%O A133879 0,10
%A A133879 _Hieronymus Fischer_, Oct 10 2007