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A327545 Triangle T(n,k) read by rows giving the number of zeroless polydivisible numbers in base n that have k distinct digits with 1 <= k <= n-1. 4
1, 4, 0, 5, 2, 2, 10, 14, 8, 0, 7, 14, 20, 2, 2, 26, 39, 84, 60, 27, 0, 11, 47, 108, 95, 63, 3, 3, 20, 101, 233, 369, 289, 79, 17, 0, 19, 86, 306, 475, 714, 409, 146, 1, 1, 32, 201, 979, 2048, 3581, 3474, 1925, 449, 51, 0, 17, 114, 507, 1273, 2224, 2239, 1074, 230, 35, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

For k >= n there is no k-digit zeroless polydivisible number in base n.

LINKS

Seiichi Manyama, Rows n = 2..18, flattened

Wikipedia, Polydivisible number.

EXAMPLE

n | zeroless polydivisible numbers in base n

--+------------------------------------------

2 | [1]

3 | [1, 2, 11, 22]

4 | [1, 2, 3, 22, 222],  [12, 32], [123, 321]

So T(2,1) = 1, T(3,1) = 4, T(3,2) = 0, T(4,1) = 5, T(4,2) = 2, T(4,3) = 2.

Triangle begins:

n\k  |  1    2    3    4    5    6    7  8  9

-----+----------------------------------------

   2 |  1;

   3 |  4,   0;

   4 |  5,   2,   2;

   5 | 10,  14,   8,   0;

   6 |  7,  14,  20,   2,   2;

   7 | 26,  39,  84,  60,  27,   0;

   8 | 11,  47, 108,  95,  63,   3,   3;

   9 | 20, 101, 233, 369, 289,  79,  17, 0;

  10 | 19,  86, 306, 475, 714, 409, 146, 1, 1;

PROG

(Ruby)

def A(n)

  d = 0

  a = (1..n - 1).map{|i| [i]}

  ary = [n - 1] + Array.new(n - 2, 0)

  while d < n - 2

    d += 1

    b = []

    a.each{|i|

      (1..n - 1).each{|j|

        m = i.clone + [j]

        if (0..d).inject(0){|s, k| s + m[k] * n ** (d - k)} % (d + 1) == 0

          b << m

          ary[m.uniq.size - 1] += 1

        end

      }

    }

    a = b

  end

  ary

end

def A327545(n)

  (2..n).map{|i| A(i)}.flatten

end

p A327545(10)

CROSSREFS

Row sums give A324020.

T(2*n,2*n-1) gives A181736.

T(n,1) gives A327577.

Cf. A324019, A324205.

Sequence in context: A309215 A309216 A083745 * A306072 A185199 A201196

Adjacent sequences:  A327542 A327543 A327544 * A327546 A327547 A327548

KEYWORD

nonn,base,tabl

AUTHOR

Seiichi Manyama, Sep 16 2019

STATUS

approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)