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A253942
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a(n) = 3*binomial(n+1, 5).
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2
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3, 18, 63, 168, 378, 756, 1386, 2376, 3861, 6006, 9009, 13104, 18564, 25704, 34884, 46512, 61047, 79002, 100947, 127512, 159390, 197340, 242190, 294840, 356265, 427518, 509733, 604128, 712008, 834768, 973896, 1130976, 1307691, 1505826, 1727271, 1974024, 2248194
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OFFSET
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4,1
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COMMENTS
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For a set of integers {1,2,...,n}, a(n) is the sum of the 2 smallest elements of each subset with 4 elements, which is 3*binomial(n+1, 5) (for n >= 4), hence a(n) = 3*binomial(n+1, 5) = 3*A000389(n+1).
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LINKS
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FORMULA
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a(n) = (n-3)*(n-2)*(n-1)*n*(1+n)/40. - Colin Barker, Jan 20 2015
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EXAMPLE
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For A={1,2,3,4}, the only subset with 4 elements is {1,2,3,4}; sum of 2 minimum elements of this subset: a(4) = 1+2 = 3 = 3*binomial(4+1, 5).
For A={1,2,3,4,5}, the 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 2 smallest elements of each subset: a(5) = (1+2)+(1+2)+(1+2)+(1+3)+(2+3) = 18 = 3*binomial(5+1, 5).
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MATHEMATICA
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a253942[n_] := Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {4}]] & /@ Range@ n, 3]; a253942[28] (* Michael De Vlieger, Jan 20 2015 *)
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PROG
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(PARI) Vec(3*x^4/(x-1)^6 + O(x^100)) \\ Colin Barker, Jan 20 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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