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

0,10

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.

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

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 *)

Prog

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

Crossrefs

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

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

Cf. A007318.

Sequence in context: A258478 A320756 A053309 * A002889 A055911 A087076

Adjacent sequences: A035037 A035038 A035039 * A035041 A035042 A035043

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved