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A068011
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Number of subsets of {1,2,3,...,n} that sum to 0 mod 5.
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1
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1, 1, 1, 2, 4, 8, 14, 26, 52, 104, 208, 412, 820, 1640, 3280, 6560, 13112, 26216, 52432, 104864, 209728, 419440, 838864, 1677728, 3355456, 6710912, 13421792, 26843552, 53687104, 107374208, 214748416, 429496768, 858993472, 1717986944
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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s(k+1) = 2s(k) if k == 2, 3, or 4 mod 5, 2s(k)-2^(k/5) if k == 0 mod 5, 2s(k)-2^((k-1)/5) if k == 1 mod 5
Empirical G.f.: -(x^2-x+1)*(2*x^3+2*x^2-1) / ((2*x-1)*(2*x^5-1)). [Colin Barker, Dec 22 2012]
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MAPLE
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A068011_rec := proc(n); if(0 = n) then RETURN(1); fi; if(1 = (n mod 5)) then RETURN(2*A068011_rec(n-1)-2^((n-1)/5)); fi; if(2 = (n mod 5)) then RETURN(2*A068011_rec(n-1)-2^((n-2)/5)); fi; RETURN(2*A068011_rec(n-1)); end;
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MATHEMATICA
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LinearRecurrence[{2, 0, 0, 0, 2, -4}, {1, 1, 1, 2, 4, 8}, 40] (* Jean-François Alcover, Mar 06 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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