A253947 a(n) = 6*binomial(n+1,7).

6, 48, 216, 720, 1980, 4752, 10296, 20592, 38610, 68640, 116688, 190944, 302328, 465120, 697680, 1023264, 1470942, 2076624, 2884200, 3946800, 5328180, 7104240, 9364680, 12214800, 15777450, 20195136, 25632288, 32277696, 40347120, 50086080, 61772832, 75721536

Offset

6,1

Comments

For a set of integers {1,2,...,n}, a(n) is the sum of the 3 smallest elements of each subset with 6 elements, which is 6*binomial(n+1,7) (for n>=6), hence a(n) = 6*binomial(n+1,7) = 6*A000580(n+1).

Links

Colin Barker, Table of n, a(n) for n = 6..1000

Serhat Bulut, Oktay Erkan Temizkan, Subset Sum Problem

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = 6*binomial(n+1,7) = 6*A000580(n+1).

G.f.: 6*x^6 / (1-x)^8. - Colin Barker, Apr 03 2015

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Wesley Ivan Hurt, Sep 03 2022

Example

For A={1,2,3,4,5,6,7}, the 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}, and {2,3,4,5,6,7}.
Sum of 3 smallest elements of each subset: a(7) = (1+2+3) + (1+2+3) + (1+2+3) + (1+2+3) + (1+2+4) + (1+3+4) + (2+3+4) = 48 = 6*binomial(7+1,7) = 6*A000580(7+1).

Mathematica

Drop[Plus @@ Flatten[Part[#, 1 ;; 3] & /@ Subsets[Range@ #, {6}]] & /@
  Range@ 30, 5] (* Michael De Vlieger, Jan 20 2015 *)
6 Binomial[Range[7, 31], 7] (* Michael De Vlieger, Feb 13 2015, after Alonso del Arte at A253946 *)

Prog

(Magma) [6*Binomial(n+1, 7): n in [6..40]]; // Vincenzo Librandi, Feb 13 2015
(PARI) Vec(6*x^6/(1-x)^8 + O(x^100)) \\ Colin Barker, Apr 03 2015

Crossrefs

Cf. A000580 (binomial(n, 7)).

Sequence in context: A254832 A026695 A208536 * A260344 A353247 A262354

Adjacent sequences: A253944 A253945 A253946 * A253948 A253949 A253950

Keyword

nonn,easy

Author

Serhat Bulut, Jan 20 2015

Extensions

More terms from Vincenzo Librandi, Feb 13 2015

Status

approved