A035038 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,5).

0, 0, 0, 0, 0, 0, 1, 8, 37, 130, 386, 1024, 2510, 5812, 12911, 27824, 58651, 121670, 249528, 507624, 1026876, 2069256, 4158861, 8344056, 16721761, 33486026, 67025182, 134116144, 268313018, 536724316, 1073567387, 2147277280, 4294724471, 8589650318, 17179537972

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Starting with "1", equals the eigensequence of a triangle with A000579 = binomial(n,6) = (1, 7, 28, 84, 210, ...) as the left column and the rest 1's. - Gary W. Adamson, Jul 24 2010

Links

• Alois P. Heinz, 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

Cf. A000079, A000225, A000295, A000579, A002663, A002664, A007318.

Cf. A035039, A035040, A035041, A035042.

Programs

Haskell

a035038 n = a035038_list !! n
a035038_list = map (sum . drop 6) a007318_tabl
-- Reinhard Zumkeller, Jun 20 2015

Magma

[n le 5 select 0 else (&+[Binomial(n,j): j in [6..n]]): n in [0..50]]; // G. C. Greubel, Mar 20 2023

Maple

a:= n-> (Matrix(7, (i,j)-> if (i=j-1) then 1 elif j=1 then [8,-27,50,-55, 36,-13,2][i] else 0 fi)^(n))[1,7]:
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 05 2008

Mathematica

Table[Sum[Binomial[n, k+6], {k,0,n}], {n,0,30}] (* Zerinvary Lajos, Jul 08 2009 *)
Table[2^n-Total[Binomial[n,Range[0,5]]],{n,0,40}] (* Harvey P. Dale, Oct 24 2017 *)

SageMath

[sum(binomial(n,j) for j in range(6,n+1)) for n in range(51)] # G. C. Greubel, Mar 20 2023

Formula

From Paul Barry, Aug 23 2004: (Start)

G.f.: x^6/((1-2*x)*(1-x)^6).

a(n) = Sum_{k=0..n} C(n, k+6) = Sum_{k=6..n} C(n, k).

a(n) = 2*a(n-1) + C(n-1, 5). (End)