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 A253945 a(n) = 6*binomial(n+1,5). 3
 6, 36, 126, 336, 756, 1512, 2772, 4752, 7722, 12012, 18018, 26208, 37128, 51408, 69768, 93024, 122094, 158004, 201894, 255024, 318780, 394680, 484380, 589680, 712530, 855036, 1019466, 1208256, 1424016, 1669536, 1947792, 2261952, 2615382, 3011652, 3454542 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS For a set of integers {1,2,...,n}, a(n) is the sum of the 3 smallest elements of each subset with 4 elements, which is 6*binomial(n+1,5) for n>=4, hence a(n) = 6*binomial(n+1,5) = 6*A000389(n+1). - Serhat Bulut, Oktay Erkan Temizkan, Jan 20 2015 LINKS Colin Barker, Table of n, a(n) for n = 4..1000 Serhat Bulut, Oktay Erkan Temizkan, Subset Sum Problem Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = 6*A000389(n+1). G.f.: 6*x^4 / (1-x)^6. - Colin Barker, Apr 03 2015 a(n) = Sum_{i=1..n-2} A000217(i-1)*A000217(i+1) with a(3)=0. [Bruno Berselli, Jul 20 2015] E.g.f.: x^4*(5 + x)*exp(x)/20. - G. C. Greubel, Nov 24 2017 EXAMPLE For A={1,2,3,4,5}, subsets with 4 elements are {1,2,3,4}, {1,2,3,5}, {1,2,4,5}, {1,3,4,5,}, {2,3,4,5}. Sum of 3 smallest elements of each subset: a(5) = (1+2+3) + (1+2+3) + (1+2+4) + (1+3+4) + (2+3+4) = 36 = 6*binomial(5+1,5) = 6*A000389(5+1). MATHEMATICA Drop[Plus @@ Flatten[Part[#, 1 ;; 3] & /@ Subsets[Range@ #, {4}]] & /@   Range@ 28, 3] (* Michael De Vlieger, Jan 20 2015 *) 6 Binomial[Range[5, 29], 5] (* Michael De Vlieger, Feb 13 2015, after Alonso del Arte at A253946 *) PROG (MAGMA) [6*Binomial(n+1, 5): n in [4..40]]; // Vincenzo Librandi, Feb 13 2015 (PARI) Vec(6*x^4/(1-x)^6 + O(x^100)) \\ Colin Barker, Apr 03 2015 CROSSREFS Cf. A000389, A000217, Sequence in context: A083374 A264366 A061707 * A056375 A321579 A018214 Adjacent sequences:  A253942 A253943 A253944 * A253946 A253947 A253948 KEYWORD nonn,easy AUTHOR Serhat Bulut, Jan 20 2015 EXTENSIONS More terms from Vincenzo Librandi, Feb 13 2015 STATUS approved

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Last modified January 21 17:42 EST 2019. Contains 319350 sequences. (Running on oeis4.)