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A184825 a(n) = n + floor(n*t) + floor(n*t^2) + floor(n/t), where t is the tetranacci constant.

%I A184825 #12 May 19 2019 14:48:26
%S A184825 5,13,20,27,34,42,49,56,63,71,77,85,92,99,105,113,120,127,134,142,149,
%T A184825 156,163,171,177,185,193,199,206,213,221,227,235,242,250,256,264,271,
%U A184825 278,285,293,299,306,313,321,327,335,342,350,356,364,371,378,386,393,400,406,414,421,428,435,443,450,457,464,472,478,486,493,500,506,514,521,528,535,543,550,557,564,572,579,586,593,600,607,614,622,628,636,643,651,657,665,672,679,686,693,700,707,714,722,728,736,743,751,757
%N A184825 a(n) = n + floor(n*t) + floor(n*t^2) + floor(n/t), where t is the tetranacci constant.
%C A184825 This is one of four sequences that partition the positive integers.
%C A184825 Given t is the tetranacci constant, then the following sequences are disjoint:
%C A184825 . A184823(n) = n + [n/t] + [n/t^2] + [n/t^3],
%C A184825 . A184824(n) = n + [n*t] + [n/t]   + [n/t^2],
%C A184825 . A184825(n) = n + [n*t] + [n*t^2] + [n/t],
%C A184825 . A184826(n) = n + [n*t] + [n*t^2] + [n*t^3], where []=floor.
%C A184825 This is a special case of _Clark Kimberling_'s results given in A184812.
%F A184825 Lim_{n->infinity} a(n)/n = t^3 = 7.1618472084864470579236869...
%F A184825 a(n) = n + floor(n*p/q) + floor(n*r/q) + floor(n*s/q), where p=t, q=t^2, r=t^3, s=t^4, and t is the tetranacci constant.
%e A184825 Let t be the tetranacci constant, then t^3 = 1 + t + t^2 + 1/t and:
%e A184825 t = 1.92756197548..., t^2 = 3.71549516932..., t^3 = 7.16184720848..., t^4 = 13.8049043532...
%t A184825 With[{t=x/.Last[Solve[x^4==Total[x^Range[0,3]],x]]},Table[n+Floor[n t]+Floor[n t^2]+Floor[n/t],{n,120}]]  (* _Harvey P. Dale_, Feb 02 2011 *)
%o A184825 (PARI) {a(n)=local(t=real(polroots(1+x+x^2+x^3-x^4)[2])); n+floor(n*t)+floor(n*t^2)+floor(n/t)}
%Y A184825 Cf. A184823, A184824, A184826; A184812, A086088.
%K A184825 nonn
%O A184825 1,1
%A A184825 _Paul D. Hanna_, Jan 23 2011