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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
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
Cf. A109783 (row lengths), A143671 (row n=10), A144688, A271374 (row sums).
Sequence in context: A058754 A279909 A125087 * A307558 A226273 A111353
KEYWORD
nonn,base,tabf
AUTHOR
Martin Renner, Apr 05 2016
EXTENSIONS
Rows n=17 to n=25 added to b-file by Max Alekseyev, Sep 11 2021
STATUS
approved