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Number of partitions of n into parts having in decimal representation mutually no common digits.
5

%I #7 Feb 17 2019 23:25:26

%S 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,

%T 82,92,92,106,105,117,123,129,132,145,153,157,173,173,187,204,214,218,

%U 250,257,266,298,301,329,359,368,370,412,433,433,478,475,508,538,526

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

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

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

%C all partitions have no more than 9 parts.

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

%C 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

%e n=20: there are A000009(20)=64 partitions into distinct

%e parts,

%e the following 23 partitions contain parts with common digits:

%e 19+1, 17+2+1, 16+3+1, 15+5, 15+4+1, 14+5+1, 14+4+2, 14+3+2+1,

%e 13+6+1, 13+4+3, 13+4+2+1, 12+7+1, 12+6+2, 12+5+2+1, 12+4+3+1,

%e 11+8+1, 11+6+2+1, 11+5+3+1, 10+9+1, 10+7+2+1, 10+6+3+1,

%e 10+5+4+1 and 10+4+3+2+1, therefore a(20) = 64 - 23 = 41.

%K nonn,base

%O 1,3

%A _Reinhard Zumkeller_, Jul 06 2005