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A253943 a(n) = 3*binomial(n+1,6). 0

%I #55 Sep 08 2022 08:46:11

%S 3,21,84,252,630,1386,2772,5148,9009,15015,24024,37128,55692,81396,

%T 116280,162792,223839,302841,403788,531300,690690,888030,1130220,

%U 1425060,1781325,2208843,2718576,3322704,4034712,4869480,5843376,6974352,8282043,9787869,11515140

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

%C 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

%H Serhat Bulut and Oktay Erkan Temizkan, <a href="https://web.archive.org/web/20160708101054/http://matematikproje.com/dosyalar/7e1cdSubset_smallest_elements_Sum.pdf">Subset Sum Problem</a>, 2015.

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

%F From _Amiram Eldar_, Jan 09 2022: (Start)

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

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

%e 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}.

%e Sum of 2 smallest elements of each subset:

%e a(6) = (1+2) + (1+2) + (1+2) + (1+2) + (1+3) + (2+3) = 21 = 3*C(6+1,6) = 3*A000579(6+1).

%t Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {5}]] & /@

%t Range@ 28, 4] (* _Michael De Vlieger_, Jan 20 2015 *)

%t 3 Binomial[Range[6, 29], 6] (* _Michael De Vlieger_, Feb 13 2015, after _Alonso del Arte_ at A253946 *)

%o (Magma) [3*Binomial(n+1,6): n in [5..40]]; // _Vincenzo Librandi_, Feb 13 2015

%Y Cf. A000579.

%K nonn

%O 5,1

%A _Serhat Bulut_, Jan 20 2015

%E More terms from _Vincenzo Librandi_, Feb 13 2015

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