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%I #33 Apr 16 2023 22:12:13
%S 1,1,3,3,2,2,2,2,3,3,1,1,0,0,0,0,1,1,3,3,2,2,2,2,3,3,1,1,0,0,0,0,1,1,
%T 3,3,2,2,2,2,3,3,1,1,0,0,0,0,1,1,3,3,2,2,2,2,3,3,1,1,0,0,0,0,1,1,3,3,
%U 2,2,2,2,3,3,1,1,0,0,0,0,1,1,3,3,2,2,2,2,3,3,1,1,0,0,0,0,1,1,3,3,2,2,2,2,3
%N a(n) = binomial(n+4,n) mod 4.
%C Periodic with length 4^2=16.
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1).
%F a(n) = binomial(n+4,4) mod 4.
%F G.f.: (1 + x + 3*x^2 + 3*x^3 + 2*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 3*x^8 + 3*x^9 + x^10 + x^11)/(1 - x^16) = (1 + 2*x^2 + 2*x^6 + x^8)/((1 - x)*(1 + x^4)*(1 + x^8)).
%F a(n) = A000505(n+5) mod 4. - _John M. Campbell_, Jul 14 2016
%F a(n) = A000506(n+6) mod 4. - _John M. Campbell_, Jul 15 2016
%e For n=2, binomial(6,2) = 6*5/2 = 15, which is 3 (mod 4) so a(2) = 3. - _Michael B. Porter_, Jul 19 2016
%t Table[Mod[Binomial[n + 4, 4], 4], {n, 0, 100}] (* _Vincenzo Librandi_, Jul 15 2016 *)
%o (Magma) [Binomial(n+4,n) mod 4: n in [0..100]]; // _Vincenzo Librandi_, Jul 15 2016
%Y Cf. A000040, A133630, A038509.
%Y Cf. A133620, A133621, A133622, A133623, A133624, A133625
%Y Cf. A133634, A133635, A133636.
%Y Cf. A133874, A133880, A133890, A133900, A133910.
%K nonn,easy
%O 0,3
%A _Hieronymus Fischer_, Oct 10 2007
%E G.f. corrected by _Bruno Berselli_, Jul 19 2016
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