|
|
A271373
|
|
Triangle T(n,k) read by rows giving the number of k-digit polydivisible numbers (see A144688) in base n with 1 <= k <= A109783(n).
|
|
3
|
|
|
2, 1, 3, 3, 3, 3, 2, 2, 4, 6, 8, 8, 7, 4, 1, 5, 10, 17, 21, 21, 21, 13, 10, 6, 4, 6, 15, 30, 45, 54, 54, 49, 46, 21, 3, 1, 7, 21, 49, 87, 121, 145, 145, 145, 121, 92, 56, 33, 20, 14, 7, 3, 1, 1, 8, 28, 74, 148, 238, 324, 367, 367, 320, 258, 188, 122, 69, 37, 12, 6, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) ~ (n-1)*n^(k-1)/k!
T(10,k) = A143671(k), 1 <= k <= 25.
|
|
EXAMPLE
|
The triangle begins
n\k 1 2 3 4 5 6 7 8 9 10 ...
2: 2 1
3: 3 3 3 3 2 2
4: 4 6 8 8 7 4 1
5: 5 10 17 21 21 21 13 10 6 4
...
|
|
MAPLE
|
b:=10; # Base
P:={seq(i, i=1..b-1)}: # Polydivisible numbers
M:=[nops(P)+1]: # Number of k-digit polydivisible numbers
for i from 2 while nops(P)>0 do
Q:={}:
for n from 1 to nops(P) do
for j from 0 to b-1 do
if P[n]*b+j mod i = 0 then Q:={op(Q), P[n]*b+j}: fi:
od:
od:
M:=[op(M), nops(Q)]:
P:=Q;
od:
T||b:=op(M[1..nops(M)-1]); # Table row T(n, k) for n = b
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|