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A375924
Number A(n,k) of partitions of [n] such that the element sum of each block is one more than a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
10
1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 5, 0, 1, 1, 0, 2, 15, 0, 1, 1, 0, 0, 4, 52, 0, 1, 1, 0, 1, 1, 10, 203, 0, 1, 1, 0, 1, 2, 3, 28, 877, 0, 1, 1, 0, 0, 0, 3, 9, 96, 4140, 0, 1, 1, 0, 0, 0, 0, 1, 17, 320, 21147, 0, 1, 1, 0, 0, 0, 1, 1, 8, 108, 1436, 115975, 0
OFFSET
0,9
LINKS
EXAMPLE
A(5,2) = 10: 12345, 124|3|5, 12|34|5, 12|3|45, 14|23|5, 1|234|5, 1|23|45, 14|25|3, 1|245|3, 1|25|34.
A(6,3) = 9: 136|25|4, 13|256|4, 13|25|46, 16|235|4, 1|2356|4, 1|235|46, 16|25|34, 1|256|34, 1|25|346.
A(7,4) = 8: 14|23|5|67, 1|234|5|67, 1|23|45|67, 1|23|467|5, 14|27|36|5, 1|247|36|5, 1|27|346|5, 1|27|36|45.
A(8,5) = 1: 12345678.
A(8,8) = 4: 18|27|36|45, 1|278|36|45, 1|27|368|45, 1|27|36|458.
A(9,6) = 87: 123469|58|7, 12349|568|7, 12349|58|67, 123568|49|7, ..., 1|25|346789, 16|289|3457, 1|2689|3457, 1|289|34567.
A(9,8) = 5: 18|27|36|45|9, 1|278|36|45|9, 1|27|368|45|9, 1|27|36|458|9, 1|27|36|45|89.
A(9,10) = 1: 1|29|38|47|56.
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...
0, 5, 2, 0, 1, 1, 0, 0, 0, 0, 0, ...
0, 15, 4, 1, 2, 0, 0, 0, 1, 1, 0, ...
0, 52, 10, 3, 3, 0, 1, 1, 0, 0, 0, ...
0, 203, 28, 9, 1, 1, 3, 0, 0, 1, 1, ...
0, 877, 96, 17, 8, 15, 4, 0, 1, 1, 0, ...
0, 4140, 320, 108, 32, 1, 0, 1, 4, 0, 0, ...
0, 21147, 1436, 324, 51, 10, 87, 72, 5, 0, 1, ...
0, 115975, 5556, 1409, 621, 50, 1, 0, 0, 1, 5, ...
CROSSREFS
Rows n=1-2 give: A000012, A033322 (for k>=1).
Main diagonal gives A142150 (for n>=2).
A(n+1,n) gives A158416 (for n>=2).
A(n,n+1) gives A135528(n+1).
Sequence in context: A262124 A199954 A333580 * A219987 A077614 A336396
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 02 2024
STATUS
approved