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URL: https://oeis.org/A253946

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A253946
a(n) = 6*binomial(n+1, 6).
7
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
5,1
COMMENTS
For a set of integers {1, 2, ..., n}, a(n) is the sum of the 3 smallest elements of each subset with 5 elements, which is 6*C(n+1, 6) (for n >= 5), hence a(n) = 6*C(n+1, 6) = 6 * A000579(n+1).
LINKS
Serhat Bulut and Oktay Erkan Temizkan, Subset Sum Problem, 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)
EXAMPLE
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).
MAPLE
A253946:=n->6*binomial(n+1, 6): seq(A253946(n), n=5..50); # Wesley Ivan Hurt, Feb 13 2015
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 *)
PROG
(Magma) [6*Binomial(n+1, 6): n in [5..40]]; // Vincenzo Librandi, Feb 13 2015
(PARI) Vec(6*x^5/(1-x)^7 + O(x^100)) \\ Colin Barker, Apr 03 2015
CROSSREFS
Cf. A000579.
Sixth column of A003506.
Sequence in context: A169938 A082986 A180806 * A359847 A062136 A047663
KEYWORD
nonn,easy
AUTHOR
Serhat Bulut, Jan 20 2015
EXTENSIONS
More terms from Vincenzo Librandi, Feb 13 2015
STATUS
approved