A096302 Number of combinations of two natural numbers that together have n digits.

81, 1620, 24300, 324000, 4050000, 48600000, 567000000, 6480000000, 72900000000, 810000000000, 8910000000000, 97200000000000, 1053000000000000, 11340000000000000, 121500000000000000, 1296000000000000000

Offset: 2

Author

Hagai Helman (Helman(AT)actcom.net.il), Jun 25 2004

Keywords

• nonn
• easy
• base

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..100

Crossrefs

Cf. A053541.

Programs

Magma

[81*(n-1)*10^(n-2): n in [2..30]]; // Vincenzo Librandi, Jun 06 2011

Mathematica

f[n_] := Sum[Binomial[n - 1, i]*9^(i + 1)*i, {i, 0, n}]; Table[ a[n], {n, 2, 17}] (* Robert G. Wilson v, Jun 30 2004 *)

Formula

a(n) = Sum_{i=0..n-1} binomial(n-1, i)*9^(i+1)*i.

a(n) = 81*(n-1)*10^(n-2). - Vladeta Jovovic, Jun 26 2004

Extensions

More terms from Robert G. Wilson v, Jun 30 2004