A253943 a(n) = 3*binomial(n+1,6).

3, 21, 84, 252, 630, 1386, 2772, 5148, 9009, 15015, 24024, 37128, 55692, 81396, 116280, 162792, 223839, 302841, 403788, 531300, 690690, 888030, 1130220, 1425060, 1781325, 2208843, 2718576, 3322704, 4034712, 4869480, 5843376, 6974352, 8282043, 9787869, 11515140

Offset

5,1

Comments

For a set of integers {1,2,...,n}, a(n) is the sum of the 2 smallest elements of each subset with 5 elements, which is 3*C(n+1,6) (for n>=5), hence a(n) = 3*C(n+1,6) = 3*A000579(n+1). - Serhat Bulut, Oktay Erkan Temizkan, Jan 20 2015

Links

Table of n, a(n) for n=5..39.

Serhat Bulut and Oktay Erkan Temizkan, Subset Sum Problem, 2015.

Formula

a(n) = 3*C(n+1,6) = 3*A000579(n+1).

From Amiram Eldar, Jan 09 2022: (Start)

Sum_{n>=5} 1/a(n) = 2/5.

Sum_{n>=5} (-1)^(n+1)/a(n) = 64*log(2) - 661/15. (End)

Example

For A={1,2,3,4,5,6} subsets with 5 elements are {1,2,3,4,5}, {1,2,3,4,6}, {1,2,3,5,6}, {1,2,4,5,6}, {1,3,4,5,6}, {2,3,4,5,6}.
Sum of 2 smallest elements of each subset:
a(6) = (1+2) + (1+2) + (1+2) + (1+2) + (1+3) + (2+3) = 21 = 3*C(6+1,6) = 3*A000579(6+1).

Mathematica

Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {5}]] & /@
  Range@ 28, 4] (* Michael De Vlieger, Jan 20 2015 *)
3 Binomial[Range[6, 29], 6] (* Michael De Vlieger, Feb 13 2015, after Alonso del Arte at A253946 *)

Prog

(Magma) [3*Binomial(n+1, 6): n in [5..40]]; // Vincenzo Librandi, Feb 13 2015

Crossrefs

Cf. A000579.

Sequence in context: A176646 A102832 A112851 * A034490 A071351 A083231

Adjacent sequences: A253940 A253941 A253942 * A253944 A253945 A253946

Keyword

nonn

Author

Serhat Bulut, Jan 20 2015

Extensions

More terms from Vincenzo Librandi, Feb 13 2015

Status

approved