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

0, 1, 10, 56, 240, 880, 2912, 8960, 26112, 72960, 197120, 518144, 1331200, 3354624, 8314880, 20316160, 49020928, 116981760, 276430848, 647495680, 1504706560, 3471835136, 7958691840, 18136170496, 41104179200, 92694118400, 208071032832

Offset

0,3

Comments

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.

Links

Matthew House, Table of n, a(n) for n = 0..3272

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

a(n) = 2^(n - 2)*n*(n + 1)*(2*n + 1)/3.

G.f.: x*(1 + 2*x)/(1 - 2*x)^4.

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Matthew House, Feb 13 2017

a(n) = (1/2) * Sum_{k=0..n} Sum_{i=0..n} i^2 * C(n,k). - Wesley Ivan Hurt, Sep 21 2017

Example

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.

Prog

(PARI) a(n) = (2^(n-2))*n*(n+1)*(2*n+1)/3 \\ Michel Marcus, Jul 12 2013

Crossrefs

Cf. A058645 has the same then similar initial values.

Equals A014483 shifted right.

Sequence in context: A035040 A002889 A055911 * A014483 A116971 A200054

Adjacent sequences: A087073 A087074 A087075 * A087077 A087078 A087079

Keyword

nonn,easy

Author

Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 08 2003

Status

approved