A173329 - OEIS

%I #19 Apr 15 2024 03:26:26

%S 1,1,1,2,2,3,3,4,5,5,6,7,8,8,10,10,11,12,12,14,13,15,15,16,17,17,19,

%T 19,21,21,23,24,25,27,27,30,30,32,33,34,36,36,38,38,40,40,41,42,42,44,

%U 43,45,45,46,47,47,49,49,51,51,53,54,55,57,57,60,60,62,63

%N a(n) = a(n-2) + a(n-3) - floor(a(n-3)/2) - floor(a(n-6)/2).

%C This sequence is interesting because in the graph of a(n+1)/a(n) there are four modes all approaching one at different rates.

%H Bo Gyu Jeong, <a href="/A173329/b173329.txt">Table of n, a(n) for n = 0..2010</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,1,-1).

%F a(n+30) = a(n)+30 for n>=12.

%F From _Chai Wah Wu_, Apr 14 2024: (Start)

%F a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-6) + a(n-8) + a(n-9) - a(n-10) for n > 21.

%F G.f.: (x^21 - x^20 + x^18 - x^16 + x^14 - x^13 + x^11 - x^9 + x^7 - x^2 + 1)/(x^10 - x^9 - x^8 + x^6 + x^4 - x^2 - x + 1). (End)

%t f[-4] = 0; f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;

%t f[n_] := f[n] = f[n - 2] + f[n - 3] - Floor[f[n - 3]/2] - Floor[f[n - 6]/2]

%t Table[f[n], {n, 0, 50}]

%K nonn

%O 0,4

%A _Roger L. Bagula_, Nov 22 2010

%E More terms from _Bo Gyu Jeong_, Jun 15 2012