A381236 Irregular triangle read by rows: to get row n, take all the numbers that can be obtained by permuting the digits of 9*n, divide them by 9, and arrange them in order.

0, 1, 2, 9, 3, 8, 4, 7, 5, 6, 5, 6, 4, 7, 3, 8, 2, 9, 1, 10, 11, 2, 9, 12, 20, 89, 90, 13, 19, 79, 14, 18, 24, 29, 68, 69, 15, 17, 35, 39, 57, 59, 16, 46, 49, 15, 17, 35, 39, 57, 59, 14, 18, 24, 29, 68, 69, 13, 19, 79, 2, 9, 12, 20, 89, 90, 21, 22, 91, 99, 102, 109

Offset

0,3

Comments

Suggested by Problem 3(c) of Carter and Russell (1994), pages 12 and 316, to which the answer is row 96 of the present triangle.

References

P. J. Carter and K. R. Russell, The IQ Challenge, Barnes and Noble, NY, 1994.

Links

Alois P. Heinz, Rows n = 0..1800, flattened

Example

  k       9*k     Permutations            Divide by 9             Sum
                                          (this sequence)         (A381237)
  0       0       0                       0                       0
  1       9       9                       1                       1
  2       18      18,81                   2,9                     11
  3       27      27,72                   3,8                     11
  4       36      36,63                   4,7                     11
  5       45      45,54                   5,6                     11
  6       54      45,54                   5,6                     11
  7       63      36,63                   4,7                     11
  8       72      27,72                   3,8                     11
  9       81      18,81                   2,9                     11
  10      90      9,90                    1,10                    11
  11      99      99                      11                      11
  12      108     18,81,108,180,801,810   2,9,12,20,89,90         222
  13      117     117,171,711             13,19,79                111
  14      126     126,162,216,261,612,621 14,18,24,29,68,69       222

Maple

T:= n-> sort(map(x-> parse(cat(x[]))/9,
    combinat[permute](convert(9*n, base, 10))))[]:
seq(T(n), n=0..25);  # Alois P. Heinz, Mar 17 2025

Crossrefs

See A381237 for row sums.

Sequence in context: A199604 A260525 A366249 * A394171 A302973 A258403

Adjacent sequences: A381233 A381234 A381235 * A381237 A381238 A381239

Keyword

nonn,tabf,base

Author

N. J. A. Sloane, Mar 16 2025

Status

approved