A035041 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,8).

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 67, 299, 1093, 3473, 9949, 26333, 65536, 155382, 354522, 784626, 1695222, 3593934, 7507638, 15505590, 31746651, 64574877, 130712029, 263644133, 530396371, 1065084887, 2136022699, 4279934123, 8570386546

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Crossrefs

a(n)= A055248(n, 9). Partial sums of A035040.

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

Cf. A007318.

Programs

Haskell

a035041 n = a035041_list !! n
a035041_list = map (sum . drop 9) a007318_tabl
-- Reinhard Zumkeller, Jun 20 2015

Maple

a:=n->sum(binomial(n,j),j=9..n): seq(a(n), n=0..33); # Zerinvary Lajos, Jan 04 2007

Mathematica

a=1;lst={};s1=s2=s3=s4=s5=s6=s7=s8=s9=0;Do[s1+=a;s2+=s1;s3+=s2;s4+=s3;s5+=s4;s6+=s5;s7+=s6;s8+=s7;s9+=s8;AppendTo[lst,s9];a=a*2,{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 10 2009 *)
Table[Sum[ Binomial[n, k], {k, 9, n}], {n, 0, 33}] (* Zerinvary Lajos, Jul 08 2009 *)

Formula

G.f.: x^9/((1-2*x)*(1-x)^9).