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!)
A322596 Square array read by descending antidiagonals (n >= 0, k >= 0): let b(n,k) = (n+k)!/((n+1)!*k!); then T(n,k) = b(n,k) if b(n,k) is an integer, and T(n,k) = floor(b(n,k)) + 1 otherwise. 1
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 4, 3, 1, 1, 1, 3, 5, 5, 3, 1, 1, 1, 4, 7, 9, 7, 4, 1, 1, 1, 4, 10, 14, 14, 10, 4, 1, 1, 1, 5, 12, 21, 26, 21, 12, 5, 1, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 1, 6, 19, 42, 66, 77, 66, 42, 19, 6, 1, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
For n >= 1, T(n,k) is the number of nodes in n-dimensional space for Mysovskikh's cubature formula which is exact for any polynomial of degree k of n variables.
LINKS
Ivan P. Mysovskikh, On the construction of cubature formulae for very simple domains, USSR Computational Mathematics and Mathematical Physics, Volume 4, Issue 1, 1964, 1-17.
EXAMPLE
Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ...
1, 1, 2, 4, 5, 7, 10, 12, 15, 19, ...
1, 1, 3, 5, 9, 14, 21, 30, 42, 55, ...
1, 1, 3, 7, 14, 26, 42, 66, 99, 143, ...
1, 1, 4, 10, 21, 42, 77, 132, 215, 334, ...
1, 1, 4, 12, 30, 66, 132, 246, 429, 715, ...
1, 1, 5, 15, 42, 99, 215, 429, 805, 1430, ...
1, 1, 5, 19, 55, 143, 334, 715, 1430, 2702, ...
1, 1, 6, 22, 72, 201, 501, 1144, 2431, 4862, ...
...
As triangular array, this begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 2, 2, 1, 1;
1, 3, 4, 3, 1, 1;
1, 3, 5, 5, 3, 1, 1;
1, 4, 7, 9, 7, 4, 1, 1;
1, 4, 10, 14, 14, 10, 4, 1, 1;
1, 5, 12, 21, 26, 21, 12, 5, 1, 1;
1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1;
...
PROG
(Maxima)
b(n, k) := (n + k)!/((n + 1)!*k!)$
T(n, k) := if integerp(b(n, k)) then b(n, k) else floor(b(n, k)) + 1$
create_list(T(k, n - k), n, 0, 15, k, 0, n);
CROSSREFS
Main diagonal: A000108.
Sequence in context: A208245 A309049 A274190 * A037306 A194799 A291119
KEYWORD
nonn,easy,tabl
AUTHOR
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 March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)