proposed

approved

editing

proposed

0, 1, 2, 4, 6, 10, 14, 21, 29, 11, 13, 8, 10, 18, 23, 33, 40, 55, 64, 170, 35, 244, 119, 174, 234, 303, 384, 475, 577, 1215, 180, 399, 1844, 904, 1194, 1538, 1901, 2326, 2776, 5681, 719, 1517, 2391, 9042, 4426, 5594, 6877, 8286, 9819, 20481, 2184, 4599, 7187, 10050, 33591

Andrew Howroyd, <a href="/A136460/b136460.txt">Table of n, a(n) for n = 1..10000</a>

a(12) = #{9+3,8+4,7+5,6+6,6+3+3,5+4+3,4+4+4,3+3+3+3} = 8;

a(13) = #{9+4,9+2+2,8+5,7+6,7+4+2,7+2+2+2,6+5+2,5+4+4,5+4+2+2,5+2+2+2+2} = 10.

(PARI) a(n)={my(S=Set(digits(n))); polcoef(1/prod(k=1, 9, 1 - if(!setsearch(S, k), x^k) + O(x*x^n)), n)} \\ Andrew Howroyd, Feb 02 2020

Terms a(38) and beyond from Andrew Howroyd, Feb 02 2020

approved

editing

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Dec 30 2007

Number of partitions of n into parts which are not digits of n in decimal representation.

0, 1, 2, 4, 6, 10, 14, 21, 29, 11, 13, 8, 10, 18, 23, 33, 40, 55, 64, 170, 35, 244, 119, 174, 234, 303, 384, 475, 577, 1215, 180, 399, 1844, 904, 1194, 1538, 1901

1,3

a(12)=#{9+3,8+4,7+5,6+6,6+3+3,5+4+3,4+4+4,3+3+3+3}=8;

a(13)=#{9+4,9+2+2,8+5,7+6,7+4+2,7+2+2+2,6+5+2,5+4+4,5+4+2+2,5+2+2+2+2}=10.

Cf. A061827.

nonn,base

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2007

approved