

A334318


Number T(n,k) of integers in base n having exactly k distinct digits such that the number formed by the consecutive subsequence of the initial j digits is divisible by j for all j in {1,...,k}; triangle T(n,k), n>=1, 1<=k<=n, read by rows.


5



1, 2, 1, 3, 1, 0, 4, 5, 5, 2, 5, 6, 6, 1, 0, 6, 13, 18, 8, 7, 2, 7, 15, 33, 34, 16, 7, 0, 8, 25, 50, 58, 52, 21, 8, 3, 9, 28, 67, 98, 101, 57, 30, 7, 0, 10, 41, 115, 168, 220, 88, 51, 9, 4, 1, 11, 45, 134, 275, 398, 315, 220, 126, 32, 10, 0, 12, 61, 206, 428, 690, 568, 503, 158, 32, 5, 1, 0
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OFFSET

1,2


LINKS



EXAMPLE

T(4,3) = 5: 102, 120, 201, 123, 321 (written in base 4):
T(7,2) = 15: 13, 15, 20, 24, 26, 31, 35, 40, 42, 46, 51, 53, 60, 62, 64 (written in base 7)
T(10,1) = 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
T(10,10) = 1: 3816547290.
Triangle T(n,k) begins:
1;
2, 1;
3, 1, 0;
4, 5, 5, 2;
5, 6, 6, 1, 0;
6, 13, 18, 8, 7, 2;
7, 15, 33, 34, 16, 7, 0;
8, 25, 50, 58, 52, 21, 8, 3;
9, 28, 67, 98, 101, 57, 30, 7, 0;
10, 41, 115, 168, 220, 88, 51, 9, 4, 1;
11, 45, 134, 275, 398, 315, 220, 126, 32, 10, 0;
12, 61, 206, 428, 690, 568, 503, 158, 32, 5, 1, 0;
...


MAPLE

b:= proc(n, s, w) option remember; `if`(s={}, 0, (k> add((t>
`if`(t=0, x, `if`(irem(t, k)=0, b(n, s minus {j}, t)
+x^k, 0)))(w*n+j), j=s)))(1+nnops(s))
end:
T:= n> (p> seq(coeff(p, x, i), i=1..n))(b(n, {$0..n1}, 0)):
seq(T(n), n=1..14);


MATHEMATICA

b[n_, s_, w_] := b[n, s, w] = If[s == {}, 0, With[{k = 1+nLength[s]}, Sum[With[{t = w*n + j}, If[t == 0, x, If[Mod[t, k] == 0, b[n, s ~Complement~ {j}, t] + x^k, 0]]], {j, s}]]];
T[n_] := PadRight[CoefficientList[b[n, Range[0, n1], 0]/x, x], n];


CROSSREFS

Bisection of main diagonal (even part) gives A181736.


KEYWORD



AUTHOR



STATUS

approved



