login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306646 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. (k+1-x^k)/(1-x^k-x^(k+1)). 11
2, 3, 1, 4, 0, 3, 5, 0, 2, 4, 6, 0, 0, 3, 7, 7, 0, 0, 3, 2, 11, 8, 0, 0, 0, 4, 5, 18, 9, 0, 0, 0, 4, 0, 5, 29, 10, 0, 0, 0, 0, 5, 3, 7, 47, 11, 0, 0, 0, 0, 5, 0, 7, 10, 76, 12, 0, 0, 0, 0, 0, 6, 0, 4, 12, 123, 13, 0, 0, 0, 0, 0, 6, 0, 4, 3, 17, 199 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
A(0,k) = k+1 and A(n,k) = n*Sum_{j=1..floor(n/k)} binomial(j,n-k*j)/j for n > 0.
A(n,k) = (k+1)*A306713(n,k) - A306713(n-k,k) for n >= k.
EXAMPLE
A(6,1) = 6*Sum_{j=1..6} binomial(j,6-j)/j = 6*(1/3+3/2+1+1/6) = 18.
A(6,2) = 6*Sum_{j=1..3} binomial(j,6-2*j)/j = 6*(1/2+1/3) = 5.
Square array begins:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
3, 2, 0, 0, 0, 0, 0, 0, 0, 0, ...
4, 3, 3, 0, 0, 0, 0, 0, 0, 0, ...
7, 2, 4, 4, 0, 0, 0, 0, 0, 0, ...
11, 5, 0, 5, 5, 0, 0, 0, 0, 0, ...
18, 5, 3, 0, 6, 6, 0, 0, 0, 0, ...
29, 7, 7, 0, 0, 7, 7, 0, 0, 0, ...
47, 10, 4, 4, 0, 0, 8, 8, 0, 0, ...
76, 12, 3, 9, 0, 0, 0, 9, 9, 0, ...
MATHEMATICA
T[0, k_] := k + 1; T[n_, k_] := n *Sum[Binomial[j, n - k*j]/j, {j, 1, Floor[n/k]}]; Table[T[k, n - k + 1], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, Jun 21 2021 *)
CROSSREFS
Sequence in context: A253257 A127412 A304791 * A152832 A211343 A039661
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Mar 03 2019
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 11:27 EDT 2024. Contains 371681 sequences. (Running on oeis4.)