|
%I #20 Mar 17 2021 13:07:33
%S 1,2,7,14,27,45,69,101,141,191,252,323,408,506,618,746,890,1052,1233,
%T 1432,1653,1895,2159,2447,2759,3097,3462,3853,4274,4724,5204,5716,
%U 6260,6838,7451,8098,8783,9505,10265,11065,11905,12787,13712,14679,15692,16750
%N Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(n + 1)(n + 2)/6.
%C See A227012.
%H Clark Kimberling, <a href="/A227016/b227016.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) + 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-8) - 3*a(n-9) + 3*a(n-10) - a(n-11) for n > 1 (conjectured).
%F G.f.: (1 - x + 4*x^2 - 2*x^3 + 4*x^4 - x^5 + x^6 + 2*x^7 - x^8 + 3*x^9 - 3*x^10 + x^11)/((x - 1)^4 (1+x) (1+x^2) (1+x^4)) (conjectured). (G.f. found by _Peter J. C. Moses_, Jul 01 2013)
%e a(1) = floor(1/(1/1)) = 1; a(2) = floor(3/(1/2 + 1/3 + 1/4)) = 2; a(3) = floor(6/(1/5 + 1/6 + ... + 1/10)) = 7.
%t z = 200; f[x_] := f[x] = 1/x; g[n_] := g[n] = n (n + 1) (n + 2)/6; s[n_] := s[n] = Sum[f[k], {k, g[n - 1] + 1, g[n]}]; v[n_] := v[n] = (g[n] - g[n - 1])/s[n]; Table[g[n], {n, 1, z}];
%t Table[Floor[v[n]], {n, 1, z}]
%Y Cf. A227012, A227013.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jul 01 2013
|
