A337631 - OEIS

%I #12 Oct 24 2020 17:40:47

%S 0,1,10,55,228,801,2526,7387,20440,54229,139218,348111,851916,2047945,

%T 4849606,11337667,26214336,60030909,136314810,307232695,687865780,

%U 1530920881,3388997550,7465861035,16374562728,35769024421,77846282146,168845901727

%N a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,...,n}.

%C Partial sums of A036826.

%C For the sum of diameters of subsets of {1,2,...,n} see A045618.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-25,38,-28,8).

%F From _Stefano Spezia_, Sep 21 2020: (Start)

%F G.f.: x*(1 + 2*x)/((1 - x)^2*(1 - 2*x)^3).

%F a(n) = 8*a(n-1) - 25*a(n-2) + 38*a(n-3) - 28*a(n-4) + 8*a(n-5) for n > 4.

%F a(n) = 2^(n+1)*(n^2 - 4*n + 8) - 3*n - 16. (End)

%e For n = 3, the nonempty subsets of {1,2,3} are {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}; the diameters of these sets are 0,0,0,1,1,2,2 and the sum of the squares of these numbers is 10.

%Y Cf. A036826, A045618.

%K nonn,easy

%O 1,3

%A _Enrique Navarrete_, Sep 20 2020