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 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Rows n = 1..25, flattened 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+n-nops(s)) end: T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n, {\$0..n-1}, 0)): seq(T(n), n=1..14); MATHEMATICA b[n_, s_, w_] := b[n, s, w] = If[s == {}, 0, With[{k = 1+n-Length[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, n-1], 0]/x, x], n]; Array[T, 14] // Flatten (* Jean-François Alcover, Feb 11 2021, after Alois P. Heinz *) CROSSREFS Columns k=1-4 give: A000027, A334320, A333405, A333469. Row sums give A334319. Bisection of main diagonal (even part) gives A181736. Cf. A111456. Sequence in context: A359368 A353490 A226131 * A199056 A350004 A144966 Adjacent sequences: A334315 A334316 A334317 * A334319 A334320 A334321 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Apr 22 2020 STATUS approved

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Last modified October 3 10:11 EDT 2023. Contains 365859 sequences. (Running on oeis4.)