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
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 *)
PROG
(Magma) [3*Binomial(n+1, 6): n in [5..40]]; // Vincenzo Librandi, Feb 13 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Serhat Bulut, Jan 20 2015
EXTENSIONS
More terms from Vincenzo Librandi, Feb 13 2015
STATUS
approved