cp's OEIS Frontend

A184821 a(n) = n + floor(n*t) + floor(n/t), where t is the tribonacci constant.

%I A184821 #7 Mar 30 2012 18:37:25
%S A184821 2,6,9,13,16,20,22,26,29,33,36,40,43,46,50,53,57,60,63,66,70,73,77,81,
%T A184821 83,87,90,94,97,101,104,107,110,114,118,121,125,127,131,134,138,141,
%U A184821 145,147,151,155,158,162,165,168,171,175,178,182,185,189,191,195,199,202,206,209,212,215,219,222,226,229,232,236,239,243,246,250,252,256,259,263,266,270,273,276,280,283,287,290,294,296,300,303,307,311,314,317,320,324,327,331,334,337,340,344,347,351,355,357,361,364,368,371,375,378,381,384,388,392,395,399,401,405,408,412,415,419,421,425,429,432
%N A184821 a(n) = n + floor(n*t) + floor(n/t), where t is the tribonacci constant.
%C A184821 This is one of three sequences that partition the positive integers.
%C A184821 Given t is the tribonacci constant, then the following sequences are disjoint:
%C A184821 . A184820(n) = n + [n/t] + [n/t^2],
%C A184821 . A184821(n) = n + [n*t] + [n/t],
%C A184821 . A184822(n) = n + [n*t] + [n*t^2], where []=floor.
%C A184821 This is a special case of Clark Kimberling's results given in A184812.
%F A184821 Limit a(n)/n = t^2 = 3.3829757679...
%F A184821 a(n) = n + floor(n*p/q) + floor(n*r/q), where p=t, q=t^2, r=t^3, and t is the tribonacci constant (see Clark Kimberling's formula in A184812).
%e A184821 Let t be the tribonacci constant, then t^2 = 1 + t + 1/t where:
%e A184821 t = 1.8392867552..., t^2 = 3.3829757679..., t^3 = 6.2222625231...
%o A184821 (PARI) {a(n)=local(t=real(polroots(1+x+x^2-x^3)[1]));n+floor(n*t)+floor(n/t)}
%Y A184821 Cf. A184820, A184822, A184812, A058265.
%K A184821 nonn
%O A184821 1,1
%A A184821 _Paul D. Hanna_, Jan 22 2011