A253946 a(n) = 6*binomial(n+1, 6).
6, 42, 168, 504, 1260, 2772, 5544, 10296, 18018, 30030, 48048, 74256, 111384, 162792, 232560, 325584, 447678, 605682, 807576, 1062600, 1381380, 1776060, 2260440, 2850120, 3562650, 4417686, 5437152, 6645408, 8069424, 9738960, 11686752, 13948704, 16564086
Offset: 5
Examples
For A = {1, 2, 3, 4, 5, 6} the 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}.
The sum of 3 smallest elements of each subset: a(6) = (1 + 2 + 3) + (1 + 2 + 3) + (1 + 2 + 3) + (1 + 2 + 4) + (1 + 3 + 4) + (2 + 3 + 4) = 42 = 6*C(6 + 1, 6) = 6*A000579(6+1).
Links
- Colin Barker, Table of n, a(n) for n = 5..1000
- Serhat Bulut and Oktay Erkan Temizkan, Subset Sum Problem, 2015.
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Magma
[6*Binomial(n+1, 6): n in [5..40]]; // Vincenzo Librandi, Feb 13 2015
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Maple
A253946:=n->6*binomial(n+1,6): seq(A253946(n), n=5..50); # Wesley Ivan Hurt, Feb 13 2015
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Mathematica
Drop[Plus @@ Flatten[Part[#, 1 ;; 3] & /@ Subsets[Range@ #, {5}]] & /@ Range@ 30, 4] (* Michael De Vlieger, Jan 20 2015 *) 6Binomial[Range[6, 29], 6] (* Alonso del Arte, Feb 05 2015 *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{6,42,168,504,1260,2772,5544},40] (* Harvey P. Dale, May 14 2019 *) -
PARI
Vec(6*x^5/(1-x)^7 + O(x^100)) \\ Colin Barker, Apr 03 2015
Formula
a(n) = 6*C(n+1,6) = 6*A000579(n+1).
G.f.: 6*x^5 / (1-x)^7. - Colin Barker, Apr 03 2015
From Amiram Eldar, Jan 09 2022: (Start)
Sum_{n>=5} 1/a(n) = 1/5.
Sum_{n>=5} (-1)^(n+1)/a(n) = 32*log(2) - 661/30. (End)
Extensions
More terms from Vincenzo Librandi, Feb 13 2015
Comments