A035039 a(n) = 2^n - C(n,0) - C(n,1) - ... - C(n,6).

0, 0, 0, 0, 0, 0, 0, 1, 9, 46, 176, 562, 1586, 4096, 9908, 22819, 50643, 109294, 230964, 480492, 988116, 2014992, 4084248, 8243109, 16587165, 33308926, 66794952, 133820134, 267936278, 536249296, 1072973612, 2146540999

Offset

0,9

Comments

Partial sums of A035038.

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.

Index entries for linear recurrences with constant coefficients, signature (9,-35,77,-105,91,-49,15,-2).

Formula

a(n) = A055248(n,7).

G.f.: x^7/((1-2*x)*(1-x)^7).

a(n) = Sum_{k=0..n}, C(n, k+7) = Sum_{k=7..n} C(n, k); a(n) = 2a(n-1) + C(n-1, 6). - Paul Barry, Aug 23 2004

Maple

a:=n->sum(binomial(n, j), j=7..n): seq(a(n), n=0..31); # Zerinvary Lajos, Feb 12 2007

Mathematica

a=1; lst={}; s1=s2=s3=s4=s5=s6=s7=0; Do[s1+=a; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; AppendTo[lst, s7]; a=a*2, {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 10 2009 *)
Table[2^n-Total[Binomial[n, Range[0, 6]]], {n, 40}] (* or *) LinearRecurrence[ {9, -35, 77, -105, 91, -49, 15, -2}, {0, 0, 0, 0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Apr 22 2016 *)

Prog

(Haskell)
a035039 n = a035039_list !! n
a035039_list = map (sum . drop 7) a007318_tabl
-- Reinhard Zumkeller, Jun 20 2015

Crossrefs

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

Cf. A007318.

Sequence in context: A053308 A201458 A034487 * A001926 A213749 A085385

Adjacent sequences: A035036 A035037 A035038 * A035040 A035041 A035042

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved