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Number of partitions of n into parts with digital root = 1.
13

%I #8 Feb 04 2014 08:59:25

%S 1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,4,4,4,4,4,4,4,4,5,6,7,7,7,7,7,

%T 7,7,8,10,11,12,12,12,12,12,12,13,15,17,18,19,19,19,19,19,20,23,26,28,

%U 29,30,30,30,30,31,34,38,41,43,44,45,45,45,46,50,55,60,63,65,66,67,67,68

%N Number of partitions of n into parts with digital root = 1.

%C a(n) = A114102(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116376(n) - A116377(n) - A116378(n) - A114099(n).

%H Reinhard Zumkeller, <a href="/A116371/b116371.txt">Table of n, a(n) for n = 1..500</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>

%e a(18) = #{10+8x1, 18x1} = 2;

%e a(19) = #{19, 10+9x1, 19x1} = 3;

%e a(20) = #{19+1, 10+10, 10+10x1, 19x1} = 4.

%o (Haskell)

%o a116371 n = p a017173_list n where

%o p _ 0 = 1

%o p [] _ = 0

%o p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

%o -- _Reinhard Zumkeller_, Feb 04 2014

%Y Cf. A010888.

%Y A147706. [From _Reinhard Zumkeller_, Nov 11 2008]

%Y A017173, A156144, A156145. [From _Reinhard Zumkeller_, Feb 05 2009]

%K nonn,base

%O 1,10

%A _Reinhard Zumkeller_, Feb 12 2006