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

1,3

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

Links

Table of n, a(n) for n=1..61.

Example

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.

Crossrefs

Sequence in context: A100928 A240671 A034140 * A008674 A067596 A114098

Adjacent sequences: A109947 A109948 A109949 * A109951 A109952 A109953

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 06 2005

Status

approved