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%I #25 Apr 24 2023 12:19:02
%S 1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,
%T 2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,
%U 3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1,3,2,2,3,1,0,0,1
%N a(n) = binomial(n+2,n) mod 2^2.
%C Periodic with length 2^3 = 8.
%H Antti Karttunen, <a href="/A133882/b133882.txt">Table of n, a(n) for n = 0..8191</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, -1, 1, -1, 1).
%F a(n) = binomial(n+2,2) mod 2^2.
%F G.f.: (1 + 3*x + 2*x^2 + 2*x^3 + 3*x^4 + x^5)/(1-x^8).
%F G.f.: (1+x)*(1+2*x+2*x^3+x^4)/(1-x^8) = (1+2*x+2*x^3+x^4)/((1-x)*(1+x^2)*(1+x^4)).
%F a(n) = A105198(n+1). - _R. J. Mathar_, Jun 08 2008
%t Table[Mod[Binomial[n+2,n],4],{n,0,120}] (* _Harvey P. Dale_, Apr 16 2011 *)
%o (PARI) A133882(n) = (binomial(n+2,n) % 4); \\ _Antti Karttunen_, Aug 10 2017
%Y Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.
%Y Cf. A133872, A133880, A133890, A133900, A133910.
%Y For the sequence regarding "binomial(n+2, n) mod 2" see A133872.
%Y A105198 shifted once left.
%K nonn,easy
%O 0,2
%A _Hieronymus Fischer_, Oct 10 2007
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