A116690 a(n) = C(n,8) + C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).

0, 1, 3, 7, 15, 31, 63, 127, 255, 510, 1012, 1980, 3796, 7098, 12910, 22818, 39202, 65535, 106761, 169765, 263949, 401929, 600369, 880969, 1271625, 1807780, 2533986, 3505698, 4791322, 6474540, 8656936, 11460948, 15033172, 19548045

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = A000581(n) + A000580(n) + A000579(n) + A000389(n) + A000332(n) + A000292(n) + A000217(n) + n. a(n) = A000581(n) + A116082(n).

G.f. ( -x*(2*x^2 - 2*x + 1)*(2*x^4 - 4*x^3 + 6*x^2 - 4*x + 1) ) / (x-1)^9. - R. J. Mathar, Oct 21 2011

a(n) = n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6)/40320. - G. C. Greubel, Nov 25 2017

Maple

seq(sum(binomial(n, k), k=1..8), n=0..33); # Zerinvary Lajos, Dec 14 2007

Mathematica

Table[n*(n + 1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6)/40320, {n, 0, 50}] (* G. C. Greubel, Nov 25 2017 *)
Table[Total[Binomial[n, Range[8]]], {n, 0, 40}] (* Harvey P. Dale, Aug 14 2023 *)

Prog

(Sage) [binomial(n, 2)+binomial(n, 4)+binomial(n, 6)+binomial(n, 8) for n in range(1, 35)] # Zerinvary Lajos, May 17 2009
(Sage) [binomial(n, 2)+binomial(n, 4)+binomial(n, 6)+binomial(n, 8)+binomial(n, 1)+binomial(n, 3)+binomial(n, 5)+binomial(n, 7)for n in range(0, 34)] # Zerinvary Lajos, May 17 2009
(PARI) for(n=0, 30, print1(n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6 ) /40320, ", ")) \\ G. C. Greubel, Nov 25 2017
(Magma) [n*(n+1)*(25584 - 9604*n + 5264*n^2 - 1295*n^3 + 231*n^4 - 21*n^5 + n^6 ) /40320: n in [0..30]]; // G. C. Greubel, Nov 25 2017

Crossrefs

Sequence in context: A245269 A043747 A105754 * A267258 A305493 A213247

Adjacent sequences: A116687 A116688 A116689 * A116691 A116692 A116693

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 15 2006

Status

approved