A109950 Number of partitions of n into parts having in decimal representation mutually no common digits.

1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 14, 16, 18, 23, 25, 29, 32, 39, 41, 49, 51, 57, 66, 71, 74, 82, 92, 92, 106, 105, 117, 123, 129, 132, 145, 153, 157, 173, 173, 187, 204, 214, 218, 250, 257, 266, 298, 301, 329, 359, 368, 370, 412, 433, 433, 478, 475, 508, 538, 526

Offset: 1

Author

Reinhard Zumkeller, Jul 06 2005

Keywords

• nonn
• base

Comments

A109968(n) <= a(n) <= A000009(n);

A109951(n) = a(n+1) - a(n);

all partitions have no more than 9 parts.

a(n) <= A000009(n), a(n) < A000009(n) for n>10.

a(9876543210) = 1 and a(n) = 0 for n > 9876543210; problem: what is the smallest n such that a(n) = 0?. - Reinhard Zumkeller, Apr 11 2006

Examples

			n=20: there are A000009(20)=64 partitions into distinct
parts,
the following 23 partitions contain parts with common digits:
19+1, 17+2+1, 16+3+1, 15+5, 15+4+1, 14+5+1, 14+4+2, 14+3+2+1,
13+6+1, 13+4+3, 13+4+2+1, 12+7+1, 12+6+2, 12+5+2+1, 12+4+3+1,
11+8+1, 11+6+2+1, 11+5+3+1, 10+9+1, 10+7+2+1, 10+6+3+1,
10+5+4+1 and 10+4+3+2+1, therefore a(20) = 64 - 23 = 41.