A035040 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,7).

0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 56, 232, 794, 2380, 6476, 16384, 39203, 89846, 199140, 430104, 910596, 1898712, 3913704, 7997952, 16241061, 32828226, 66137152, 132932104, 266752238, 534688516, 1070937812, 2143911424, 4290452423

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• changed

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.

Crossrefs

a(n)= A055248(n, 8). Partial sums of A035039.

Cf. A000079, A000225, A000295, A002663, A002664, A035038-A035042.

Cf. A007318.

Programs

Haskell

a035040 n = a035040_list !! n
a035040_list = map (sum . drop 8) a007318_tabl
-- Reinhard Zumkeller, Jun 20 2015

Maple

a:=n->sum(binomial(n,j),j=8..n): seq(a(n), n=0..32); # Zerinvary Lajos, Jan 04 2007

Mathematica

a=1;lst={};s1=s2=s3=s4=s5=s6=s7=s8=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;s5+=s4;s6+=s5;s7+=s6;s8+=s7;AppendTo[lst,s8];a=a*2,{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 10 2009 *)
Table[2^n-Total[Binomial[n,Range[0,7]]],{n,0,40}] (* Harvey P. Dale, Aug 27 2025 *)

Formula

G.f.: x^8/((1-2*x)*(1-x)^8).

a(n) = sum_{k=0..n} C(n, k+8) = sum_{k=8..n} C(n, k); a(n) = 2a(n-1) + C(n-1, 7). - Paul Barry, Aug 23 2004