cp's OEIS Frontend

A087076 Sums of the squares of the elements in the subsets of the integers 1 to n.

%I A087076 #20 Sep 22 2017 02:43:41
%S A087076 0,1,10,56,240,880,2912,8960,26112,72960,197120,518144,1331200,
%T A087076 3354624,8314880,20316160,49020928,116981760,276430848,647495680,
%U A087076 1504706560,3471835136,7958691840,18136170496,41104179200,92694118400,208071032832
%N A087076 Sums of the squares of the elements in the subsets of the integers 1 to n.
%C A087076 A000076 gives the number of subsets of 1 to n. A001787 gives the number of elements in the subsets. A001788 gives the sum of the elements.
%H A087076 Matthew House, <a href="/A087076/b087076.txt">Table of n, a(n) for n = 0..3272</a>
%H A087076 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F A087076 a(n) = 2^(n - 2)*n*(n + 1)*(2*n + 1)/3.
%F A087076 G.f.: x*(1 + 2*x)/(1 - 2*x)^4.
%F A087076 a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - _Matthew House_, Feb 13 2017
%F A087076 a(n) = (1/2) * Sum_{k=0..n} Sum_{i=0..n} i^2 * C(n,k). - _Wesley Ivan Hurt_, Sep 21 2017
%e A087076 a(3)=56 since the subsets of (1,2,3) are ( ) (1) (1,2) (1,3) (1,2,3) (2) (2,3) (3) and the sum of the squares of the elements in these subsets is 56.
%o A087076 (PARI) a(n) = (2^(n-2))*n*(n+1)*(2*n+1)/3 \\ _Michel Marcus_, Jul 12 2013
%Y A087076 Cf. A058645 has the same then similar initial values.
%Y A087076 Equals A014483 shifted right.
%K A087076 nonn,easy
%O A087076 0,3
%A A087076 Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 08 2003