A035039 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,6).
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
Offset: 0
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
- J. Eckhoff, Der Satz von Radon in konvexen Produktstrukturen II, Monat. f. Math., 73 (1969), 7-30.
- Ângela Mestre, José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.
- Index entries for linear recurrences with constant coefficients, signature (9,-35,77,-105,91,-49,15,-2).
Programs
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Haskell
a035039 n = a035039_list !! n a035039_list = map (sum . drop 7) a007318_tabl -- Reinhard Zumkeller, Jun 20 2015
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Maple
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
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 *)
Formula
a(n) = A055248(n,7).
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
Comments