This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253943 #60 Apr 06 2025 15:00:01
%S A253943 3,21,84,252,630,1386,2772,5148,9009,15015,24024,37128,55692,81396,
%T A253943 116280,162792,223839,302841,403788,531300,690690,888030,1130220,
%U A253943 1425060,1781325,2208843,2718576,3322704,4034712,4869480,5843376,6974352,8282043,9787869,11515140
%N A253943 a(n) = 3*binomial(n+1,6).
%C A253943 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 A253943 G. C. Greubel, <a href="/A253943/b253943.txt">Table of n, a(n) for n = 5..1000</a>
%H A253943 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.
%H A253943 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A253943 a(n) = 3*C(n+1,6) = 3*A000579(n+1).
%F A253943 From _Amiram Eldar_, Jan 09 2022: (Start)
%F A253943 Sum_{n>=5} 1/a(n) = 2/5.
%F A253943 Sum_{n>=5} (-1)^(n+1)/a(n) = 64*log(2) - 661/15. (End)
%F A253943 From _G. C. Greubel_, Apr 03 2025: (Start)
%F A253943 G.f.: 3*x^5/(1-x)^7.
%F A253943 E.g.f.: (3/6!)*x^5*(x+6)*exp(x). (End)
%e A253943 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 A253943 Sum of 2 smallest elements of each subset:
%e A253943 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 A253943 Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {5}]] & /@
%t A253943 Range@ 28, 4] (* _Michael De Vlieger_, Jan 20 2015 *)
%t A253943 3 Binomial[Range[6, 29], 6] (* _Michael De Vlieger_, Feb 13 2015, after _Alonso del Arte_ at A253946 *)
%o A253943 (Magma) [3*Binomial(n+1,6): n in [5..40]]; // _Vincenzo Librandi_, Feb 13 2015
%o A253943 (SageMath)
%o A253943 def A253943(n): return 3*binomial(n+1,6)
%o A253943 print([A253943(n) for n in range(5,51)]) # _G. C. Greubel_, Apr 03 2025
%Y A253943 Cf. A000579.
%K A253943 nonn
%O A253943 5,1
%A A253943 _Serhat Bulut_, Jan 20 2015
%E A253943 More terms from _Vincenzo Librandi_, Feb 13 2015