login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316409 Number of multisets of exactly eight nonempty binary words with a total of n letters such that no word has a majority of 0's. 2
1, 3, 10, 33, 98, 291, 826, 2320, 6342, 17133, 45504, 119580, 310416, 798196, 2033289, 5136803, 12878647, 32056022, 79277444, 194822462, 476101571, 1156995495, 2797803485, 6731961588, 16126628466, 38459836055, 91355046531, 216126089962, 509445131238 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..1000

FORMULA

a(n) = [x^n y^8] 1/Product_{j>=1} (1-y*x^j)^A027306(j).

MAPLE

g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):

b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(

       binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 9)

    end:

a:= n-> coeff(b(n$2), x, 8):

seq(a(n), n=8..36);

CROSSREFS

Column k=8 of A292506.

Cf. A027306, A292549.

Sequence in context: A316406 A316407 A316408 * A316410 A316411 A292549

Adjacent sequences:  A316406 A316407 A316408 * A316410 A316411 A316412

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 02 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)