A380860 Triangle read by rows: T(n,m) (0<=m<=n) = number of positive n-digit numbers that have exactly m copies of a specific, previously selected positive base-10 digit among its digits.

1, 8, 1, 72, 17, 1, 648, 225, 26, 1, 5832, 2673, 459, 35, 1, 52488, 29889, 6804, 774, 44, 1, 472392, 321489, 91125, 13770, 1170, 53, 1, 4251528, 3365793, 1141614, 215055, 24300, 1647, 62, 1, 38263752, 34543665, 13640319, 3077109, 433755, 39123, 2205, 71, 1, 344373768, 349156737, 157306536, 41334300, 6980904, 785862, 58968, 2844, 80, 1

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).

Formula

T(n,m) = floor(9^(n-m)*(binomial(n-1,m-1)+8/9*binomial(n-1,m))), considering binomial(k,-1)=0 for k>=0 and binomial(k,l)=0 for k>=0 with k<l.

Example

Rows n=0..7 of the triangle are:
        1;
        8,       1;
       72,      17,       1;
      648,     225,      26,      1;
     5832,    2673,     459,     35,     1;
    52488,   29889,    6804,    774,    44,    1;
   472392,  321489,   91125,  13770,  1170,   53,  1;
  4251528, 3365793, 1141614, 215055, 24300, 1647, 62, 1;
  ...

Maple

seq(lprint(seq(floor(9^(n-m)*(binomial(n-1, m-1)+(8/9)*binomial(n-1, m))), m=0..n)), n=0..7);

Mathematica

A380860[n_, m_] := Floor[9^(n-m)*(Binomial[n-1, m-1] + 8/9*Binomial[n-1, m])];
Table[A380860[n, m], {n, 0, 10}, {m, 0, n}] (* Paolo Xausa, Feb 07 2025 *)

Crossrefs

Row sums give A052268 (for n>=1).

Columns k=0-1 give: A055275, A081044(n-1) (for n>=1).

Sequence in context: A038279 A075503 A260040 * A051379 A143499 A114152

Adjacent sequences: A380856 A380857 A380858 * A380861 A380862 A380863

Keyword

nonn,base,tabl,new

Author

Peter Starek, Feb 06 2025

Status

approved