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a(n) = binomial(n+9,n) mod 9.
3

%I #14 Apr 16 2023 22:12:59

%S 1,1,1,4,4,4,1,1,1,2,2,2,8,8,8,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,7,7,7,4,

%T 4,4,5,5,5,2,2,2,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,1,1,1,7,7,7,8,8,8,5,5,

%U 5,8,8,8,0,0,0,0,0,0,0,0,0,1,1,1,4,4,4,1,1,1,2,2,2,8,8,8,2,2,2,3,3,3,3,3,3

%N a(n) = binomial(n+9,n) mod 9.

%C Periodic with length 9^2 = 81.

%H <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 a(n) = binomial(n+9,9) mod 9.

%t Table[Mod[Binomial[n+9,n],9],{n,0,110}] (* _Harvey P. Dale_, Jan 14 2012 *)

%Y Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

%Y Cf. A133879, A133880, A133890, A133900, A133910.

%K nonn

%O 0,4

%A _Hieronymus Fischer_, Oct 10 2007