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A035039
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a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,6).
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10
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0, 0, 0, 0, 0, 0, 0, 1, 9, 46, 176, 562, 1586, 4096, 9908, 22819, 50643, 109294, 230964, 480492, 988116, 2014992, 4084248, 8243109, 16587165, 33308926, 66794952, 133820134, 267936278, 536249296, 1072973612, 2146540999
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OFFSET
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0,9
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COMMENTS
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LINKS
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FORMULA
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G.f.: x^7/((1-2*x)*(1-x)^7).
a(n) = Sum_{k=0..n}, C(n, k+7) = Sum_{k=7..n} C(n, k); a(n) = 2a(n-1) + C(n-1, 6). - Paul Barry, Aug 23 2004
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MAPLE
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a:=n->sum(binomial(n, j), j=7..n): seq(a(n), n=0..31); # Zerinvary Lajos, Feb 12 2007
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MATHEMATICA
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a=1; lst={}; s1=s2=s3=s4=s5=s6=s7=0; Do[s1+=a; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; AppendTo[lst, s7]; a=a*2, {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 10 2009 *)
Table[2^n-Total[Binomial[n, Range[0, 6]]], {n, 40}] (* or *) LinearRecurrence[ {9, -35, 77, -105, 91, -49, 15, -2}, {0, 0, 0, 0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Apr 22 2016 *)
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PROG
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(Haskell)
a035039 n = a035039_list !! n
a035039_list = map (sum . drop 7) a007318_tabl
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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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