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
Examples
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).
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).
Crossrefs
Cf. A000580 (binomial(n, 7)).
Programs
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Magma
[6*Binomial(n+1, 7): n in [6..40]]; // Vincenzo Librandi, Feb 13 2015
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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 *) -
PARI
Vec(6*x^6/(1-x)^8 + O(x^100)) \\ Colin Barker, Apr 03 2015
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
Extensions
More terms from Vincenzo Librandi, Feb 13 2015
Comments