login
A337631
a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,...,n}.
0
0, 1, 10, 55, 228, 801, 2526, 7387, 20440, 54229, 139218, 348111, 851916, 2047945, 4849606, 11337667, 26214336, 60030909, 136314810, 307232695, 687865780, 1530920881, 3388997550, 7465861035, 16374562728, 35769024421, 77846282146, 168845901727
OFFSET
1,3
COMMENTS
Partial sums of A036826.
For the sum of diameters of subsets of {1,2,...,n} see A045618.
FORMULA
From Stefano Spezia, Sep 21 2020: (Start)
G.f.: x*(1 + 2*x)/((1 - x)^2*(1 - 2*x)^3).
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.
a(n) = 2^(n+1)*(n^2 - 4*n + 8) - 3*n - 16. (End)
EXAMPLE
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.
CROSSREFS
Sequence in context: A290893 A034241 A341223 * A249460 A022575 A202481
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Sep 20 2020
STATUS
approved