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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.)