OFFSET
6,1
COMMENTS
For a set of integers {1,2,...,n}, a(n) is the sum of the 2 smallest elements of each subset with 6 elements, which is 3*C(n+1,7) (for n>=6), hence a(n) = 3*C(n+1,7) = 3*A000580(n+1).
LINKS
Serhat Bulut and Oktay Erkan Temizkan, Subset Sum Problem
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = 3*C(n+1,7) = 3*A000580(n+1).
a(n) = 3*C(n+1,7) = (n^7 - 14n^6 + 70n^5 - 140n^4 + 49n^3 + 154n^2 - 120n)/1680.
EXAMPLE
For A={1,2,3,4,5,6,7}, subsets with 6 elements are {1,2,3,4,5,6}, {1,2,3,4,5,7}, {1,2,3,4,6,7}, {1,2,3,5,6,7}, {1,2,4,5,6,7}, {1,3,4,5,6,7}, {2,3,4,5,6,7}.
Sum of 2 smallest elements of each subset:
a(7) = (1+2)+(1+2)+(1+2)+(1+2)+(1+2)+(1+3)+(2+3) = 24 = 3*C(7+1,7) = 3*A000580(7+1).
MATHEMATICA
Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {6}]] & /@
Range@ 28, 5] (* Michael De Vlieger, Jan 20 2015 *)
PROG
(PARI) a(n)=3*binomial(n+1, 7) \\ Charles R Greathouse IV, Feb 04 2015
(Magma) [3*Binomial(n+1, 7): n in [6..40]]; // Vincenzo Librandi, Feb 13 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Serhat Bulut, Jan 20 2015
EXTENSIONS
More terms from Vincenzo Librandi, Feb 13 2015
STATUS
approved