A068011 - OEIS

A068011

Number of subsets of {1,2,3,...,n} that sum to 0 mod 5.

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, 3435973888, 6871947776

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OFFSET

0,4

COMMENTS

For n>2, a(n) = 2 * A068031(n).

LINKS

Table of n, a(n) for n=0..35.

Sophie LeBlanc, Jan 20 2002, sci.math posting

Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,2,-4).

FORMULA

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.

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

MAPLE

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;

MATHEMATICA

LinearRecurrence[{2, 0, 0, 0, 2, -4}, {1, 1, 1, 2, 4, 8}, 40] (* Jean-François Alcover, Mar 06 2016 *)

CROSSREFS

5th row of A068009.

Sequence in context: A164169 A164166 A164161 * A048238 A048140 A179817

Adjacent sequences: A068008 A068009 A068010 * A068012 A068013 A068014

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 11 2002

STATUS

approved