A180713 - OEIS

%I #51 May 05 2024 03:30:18

%S 0,4,6,11,12,16,18,23,24,28,30,35,36,40,42,47,48,52,54,59,60,64,66,71,

%T 72,76,78,83,84,88,90,95,96,100,102,107,108,112,114,119,120,124,126,

%U 131,132,136,138,143,144,148,150,155,156,160,162,167,168,172,174,179,180,184,186,191,192,196,198,203,204

%N If n is even then a(n) = 3n, if n == 1 mod 4 then a(n) = 3n+1, if n == 3 mod 4 then a(n) = 3n+2.

%H Vincenzo Librandi, <a href="/A180713/b180713.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F From _Bruno Berselli_, Jan 23 2011: (Start)

%F G.f.:  x*(4+2*x+5*x^2+x^3)/((1-x)*(1-x^4)).

%F a(n) = (12*n+i*(i^n-(-i)^n)-3*(-1)^n+3)/4, where i is the imaginary unit.

%F a(n) = A131743(n) + 3*n. (End)

%F a(n) = +1*a(n-1)+1*a(n-4)-1*a(n-5) for n>=5. [_Joerg Arndt_, Jan 25 2011]

%p U:=n->if n mod 2 = 0 then 3*n elif n mod 4 = 1 then 3*n+1 else 3*n+2; fi;

%t fn[n_]:=Which[EvenQ[n],3n,Mod[n,4]==1,3n+1,Mod[n,4]==3,3n+2]; Array[fn,70,0] (* _Harvey P. Dale_, May 03 2013 *)

%t CoefficientList[Series[x (4 + 2 x + 5 x^2 + x^3) / ((1 - x) (1 - x^4)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 19 2013 *)

%Y A variant of A006368.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 21 2011

%E Definition corrected by _N. J. A. Sloane_, Jan 23 2011