OFFSET
6,1
COMMENTS
For a set of integers {1,2,...,n}, a(n) is the sum of the 3 smallest elements of each subset with 6 elements, which is 6*binomial(n+1,7) (for n>=6), hence a(n) = 6*binomial(n+1,7) = 6*A000580(n+1).
LINKS
Colin Barker, Table of n, a(n) for n = 6..1000
Serhat Bulut, 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) = 6*binomial(n+1,7) = 6*A000580(n+1).
G.f.: 6*x^6 / (1-x)^8. - Colin Barker, Apr 03 2015
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Wesley Ivan Hurt, Sep 03 2022
EXAMPLE
For A={1,2,3,4,5,6,7}, the 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}, and {2,3,4,5,6,7}.
Sum of 3 smallest elements of each subset: a(7) = (1+2+3) + (1+2+3) + (1+2+3) + (1+2+3) + (1+2+4) + (1+3+4) + (2+3+4) = 48 = 6*binomial(7+1,7) = 6*A000580(7+1).
MATHEMATICA
Drop[Plus @@ Flatten[Part[#, 1 ;; 3] & /@ Subsets[Range@ #, {6}]] & /@
Range@ 30, 5] (* Michael De Vlieger, Jan 20 2015 *)
PROG
(Magma) [6*Binomial(n+1, 7): n in [6..40]]; // Vincenzo Librandi, Feb 13 2015
(PARI) Vec(6*x^6/(1-x)^8 + O(x^100)) \\ Colin Barker, Apr 03 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Serhat Bulut, Jan 20 2015
EXTENSIONS
More terms from Vincenzo Librandi, Feb 13 2015
STATUS
approved