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Binomial(n+7,n) mod 7^2.
3

%I #11 Apr 26 2023 20:15:19

%S 1,8,36,22,36,8,1,2,16,23,44,23,16,2,3,24,10,17,10,24,3,4,32,46,39,46,

%T 32,4,5,40,33,12,33,40,5,6,48,20,34,20,48,6,7,7,7,7,7,7,7,8,15,43,29,

%U 43,15,8,9,23,30,2,30,23,9,10,31,17,24,17,31,10,11,39,4,46,4,39,11,12,47

%N Binomial(n+7,n) mod 7^2.

%C Periodic with length 7^3=343.

%H Ray Chandler, <a href="/A133887/b133887.txt">Table of n, a(n) for n = 0..1500</a>

%H <a href="/index/Rec#order_337">Index entries for linear recurrences with constant coefficients</a>, order 337.

%F a(n)=binomial(n+7,7) mod 7^2.

%F G.f. g(x)=sum{0<=k<343, a(k)*x^k}/(1-x^343).

%t Table[Mod[Binomial[n+7,n],49],{n,0,80}] (* _Harvey P. Dale_, Apr 08 2018 *)

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

%Y Cf. A133877, A133880, A133890, A133900, A133910.

%Y For the sequence regarding binomial(n+7, n) mod 7 see A133877.

%K nonn

%O 0,2

%A _Hieronymus Fischer_, Oct 10 2007