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A253944
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a(n) = 3*binomial(n+1,7).
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0
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3, 24, 108, 360, 990, 2376, 5148, 10296, 19305, 34320, 58344, 95472, 151164, 232560, 348840, 511632, 735471, 1038312, 1442100, 1973400, 2664090, 3552120, 4682340, 6107400, 7888725, 10097568, 12816144, 16138848, 20173560, 25043040, 30886416, 37860768
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OFFSET
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6,1
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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 6 elements, which is 3*C(n+1,7) (for n>=6), hence a(n) = 3*C(n+1,7) = 3*A000580(n+1).
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LINKS
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FORMULA
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a(n) = 3*C(n+1,7) = 3*A000580(n+1).
a(n) = 3*C(n+1,7) = (n^7 - 14n^6 + 70n^5 - 140n^4 + 49n^3 + 154n^2 - 120n)/1680.
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EXAMPLE
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For A={1,2,3,4,5,6,7}, 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}, {2,3,4,5,6,7}.
Sum of 2 smallest elements of each subset:
a(7) = (1+2)+(1+2)+(1+2)+(1+2)+(1+2)+(1+3)+(2+3) = 24 = 3*C(7+1,7) = 3*A000580(7+1).
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MATHEMATICA
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Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {6}]] & /@
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PROG
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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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EXTENSIONS
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STATUS
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approved
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