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

Author

Peter Starek, Feb 06 2025

Keywords

• nonn
• base
• tabl

Examples

			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;
  ...
		

Links

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

Crossrefs

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

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

Programs

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 *)

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

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.