A375764 a(n) is the sum of distinct sums of all subsets with two or more elements of {1, 2, ..., n}.

0, 0, 3, 18, 52, 117, 228, 403, 663, 1032, 1537, 2208, 3078, 4183, 5562, 7257, 9313, 11778, 14703, 18142, 22152, 26793, 32128, 38223, 45147, 52972, 61773, 71628, 82618, 94827, 108342, 123253, 139653, 157638, 177307, 198762, 222108, 247453, 274908, 304587

Offset

0,3

Comments

The cardinality of the set for n is A034856(n-1).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = A002817(n) - 3 for n > 1.

From Alois P. Heinz, Aug 27 2024: (Start)

G.f.: x^2*(2*x^4-7*x^3+8*x^2-3*x-3)/(x-1)^5.

a(n) = max(0,(n^4+2*n^3+3*n^2+2*n-24)/8). (End)

E.g.f.: exp(x)*(x^4/8 + x^3 + 2*x^2 + x - 3) + 2*x + 3. - Stefano Spezia, Aug 28 2024

Example

For n = 3 the starting set is {1,2,3} and there are subsets {1,2}{1,3}{2,3}{1,2,3} that sum to 3,4,5 and 6 and the sum of distinct sums (3+4+5+6) is 18.

Mathematica

Join[{0, 0}, Nest[PolygonalNumber, Range[2, 50], 2] - 3] (* Paolo Xausa, Sep 13 2024 *)

Prog

(Python)
a = lambda n: max(0, (n**4+2*n**3+3*n**2+2*n-24)//8)
print([a(n) for n in range(1, 40)])
(Python)
def A375764(n): return (m:=n*(n+1)-4)*(m+10)>>3 if n>1 else 0 # Chai Wah Wu, Aug 30 2024

Crossrefs

Cf. A002817, A034856.

Sequence in context: A064043 A267639 A238649 * A268484 A085789 A361083

Adjacent sequences: A375761 A375762 A375763 * A375765 A375766 A375767

Keyword

nonn,easy

Author

Darío Clavijo, Aug 26 2024

Extensions

More terms from Alois P. Heinz, Aug 27 2024

Status

approved