%I #52 Sep 08 2022 08:46:11
%S 3,24,108,360,990,2376,5148,10296,19305,34320,58344,95472,151164,
%T 232560,348840,511632,735471,1038312,1442100,1973400,2664090,3552120,
%U 4682340,6107400,7888725,10097568,12816144,16138848,20173560,25043040,30886416,37860768
%N a(n) = 3*binomial(n+1,7).
%C 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).
%H Serhat Bulut and Oktay Erkan Temizkan, <a href="http://matematikproje.com/dosyalar/7e1cdSubset_smallest_elements_Sum.pdf">Subset Sum Problem</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F a(n) = 3*C(n+1,7) = 3*A000580(n+1).
%F a(n) = 3*C(n+1,7) = (n^7 - 14n^6 + 70n^5 - 140n^4 + 49n^3 + 154n^2 - 120n)/1680.
%e 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}.
%e Sum of 2 smallest elements of each subset:
%e 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).
%t Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {6}]] & /@
%t Range@ 28, 5] (* _Michael De Vlieger_, Jan 20 2015 *)
%t 3 Binomial[Range[7, 29], 7] (* _Michael De Vlieger_, Feb 13 2015, after _Alonso del Arte_ at A253946 *)
%o (PARI) a(n)=3*binomial(n+1,7) \\ _Charles R Greathouse IV_, Feb 04 2015
%o (Magma) [3*Binomial(n+1, 7): n in [6..40]]; // _Vincenzo Librandi_, Feb 13 2015
%K nonn,easy
%O 6,1
%A _Serhat Bulut_, Jan 20 2015
%E More terms from _Vincenzo Librandi_, Feb 13 2015