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A035038 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,5). 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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.

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)

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

a=1; lst={}; s1=s2=s3=s4=s5=s6=0; Do[s1+=a; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; AppendTo[lst, s6]; a=a*2, {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 10 2009 *)

Table[Sum[ Binomial[n + 6, k + 6], {k, 0, n}], {n, -6, 24}] (* Zerinvary Lajos, Jul 08 2009 *)

Table[2^n-Total[Binomial[n, Range[0, 5]]], {n, 0, 40}] (* Harvey P. Dale, Oct 24 2017 *)

PROG

(Haskell)

a035038 n = a035038_list !! n

a035038_list = map (sum . drop 6) a007318_tabl

-- Reinhard Zumkeller, Jun 20 2015

CROSSREFS

Cf. A000079, A000225, A000295, A002663, A002664, A035039-A035042.

Cf. A007318.

Sequence in context: A320754 A053296 A055799 * A240188 A294372 A256412

Adjacent sequences:  A035035 A035036 A035037 * A035039 A035040 A035041

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)