|
|
A363916
|
|
Array read by descending antidiagonals. A(n, k) = Sum_{d=0..k} A363914(k, d) * n^d.
|
|
1
|
|
|
1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 2, 3, 1, 0, 0, 6, 6, 4, 1, 0, 0, 12, 24, 12, 5, 1, 0, 0, 30, 72, 60, 20, 6, 1, 0, 0, 54, 240, 240, 120, 30, 7, 1, 0, 0, 126, 696, 1020, 600, 210, 42, 8, 1, 0, 0, 240, 2184, 4020, 3120, 1260, 336, 56, 9, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,9
|
|
COMMENTS
|
Row n gives the number of n-ary sequences with primitive period k.
|
|
LINKS
|
|
|
FORMULA
|
If k > 0 then k divides A(n, k), see the transposed array of A074650.
If k > 0 then n divides A(n, k), see the transposed array of A143325.
|
|
EXAMPLE
|
Array A(n, k) starts:
[0] 1, 0, 0, 0, 0, 0, 0, 0, 0, ... A000007
[1] 1, 1, 0, 0, 0, 0, 0, 0, 0, ... A019590
[2] 1, 2, 2, 6, 12, 30, 54, 126, 240, ... A027375
[3] 1, 3, 6, 24, 72, 240, 696, 2184, 6480, ... A054718
[4] 1, 4, 12, 60, 240, 1020, 4020, 16380, 65280, ... A054719
[5] 1, 5, 20, 120, 600, 3120, 15480, 78120, 390000, ... A054720
[6] 1, 6, 30, 210, 1260, 7770, 46410, 279930, 1678320, ... A054721
[7] 1, 7, 42, 336, 2352, 16800, 117264, 823536, 5762400, ... A218124
[8] 1, 8, 56, 504, 4032, 32760, 261576, 2097144, 16773120, ... A218125
.
Triangle T(n, k) starts:
[0] 1;
[1] 0, 1;
[2] 0, 1, 1;
[3] 0, 0, 2, 1;
[4] 0, 0, 2, 3, 1;
[5] 0, 0, 6, 6, 4, 1;
[6] 0, 0, 12, 24, 12, 5, 1;
[7] 0, 0, 30, 72, 60, 20, 6, 1;
[8] 0, 0, 54, 240, 240, 120, 30, 7, 1;
|
|
MAPLE
|
for n from 0 to 9 do seq(A363916(n, k), k = 0..8) od;
|
|
PROG
|
(SageMath)
def A363916(n, k): return sum(A363914(k, d) * n^d for d in range(k + 1))
for n in range(9): print([A363916(n, k) for k in srange(9)])
def T(n, k): return A363916(k, n - k)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|