A227018 - OEIS

%I #26 Nov 03 2024 04:55:34

%S 1,3,9,24,51,95,164,266,407,598,850,1174,1582,2087,2706,3452,4342,

%T 5395,6628,8060,9714,11609,13768,16215,18975,22072,25534,29388,33662,

%U 38387,43591,49307,55568,62407,69858,77957,86740,96245,106511,117577,129482,142270

%N a(n) = floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n*(n + 1)*(n + 2)*(n + 3)/24.

%C See A227012.

%H Clark Kimberling, <a href="/A227018/b227018.txt">Table of n, a(n) for n = 1..97</a>

%F Conjectured g.f.: (-1 + x - 3 x^2 - 2 x^3 + 2 x^4 - 2 x^5 - 3 x^6 + 2 x^8 - 5 x^9 - x^12 - x^13 - 4 x^14 + 4 x^15 - 4 x^16 - 2 x^17 + 2 x^18 - 2 x^19 - 4 x^20 + 4 x^21 - 4 x^22 - x^23 - x^24 + x^25 - 4 x^26 + x^27 - x^28 - 3 x^29 + 3 x^30 - 5 x^31 - x^34 - 2 x^35 + x^36 - 3 x^37 + 2 x^38 + 2 x^39 - 2 x^40 - 3 x^41 + 6 x^42 - 3 x^43 - 3 x^44 + 6 x^45 - 4 x^46 +   x^47)/((-1 + x)^5 (1 + x) (1 + x^2) (1 - x + x^2) (1 + x + x^2) (1 - x^2 + x^4) (1 - x^3 + x^6) (1 + x^3 + x^6) (1 - x^6 + x^12)).

%e a(1) = [1/(1/1)] = 1;

%e a(2) = [4/(1/2 + 1/3 + 1/4 + 1/5)] = 3;

%e a(3) = [10/(1/6 + 1/7 + ... + 1/15)] = 9.

%t Clear[g]; g[n_] := N[Binomial[n + # - 1, #] &[4], 100]; a = {1}; Do[

%t AppendTo[a, Floor[(#2 - #1 + 1)/(HarmonicNumber[#2] - HarmonicNumber[#1 - 1])] &[g[k - 1] + 1, g[k]]], {k, 2, 100}]; a

%Y Cf. A227012, A227016.

%K nonn,easy,changed

%O 1,2

%A _Clark Kimberling_, Jul 06 2013