A337631 a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,...,n}.

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

Author

Enrique Navarrete, Sep 20 2020

Keywords

• nonn
• easy

Comments

Partial sums of A036826.

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

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-25,38,-28,8).

Crossrefs

Cf. A036826, 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)