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A116371 Number of partitions of n into parts with digital root = 1.

%I A116371 #9 Feb 16 2025 08:33:00
%S A116371 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 A116371 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 A116371 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 A116371 Number of partitions of n into parts with digital root = 1.
%C A116371 a(n) = A114102(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116376(n) - A116377(n) - A116378(n) - A114099(n).
%H A116371 Reinhard Zumkeller, <a href="/A116371/b116371.txt">Table of n, a(n) for n = 1..500</a>
%H A116371 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>
%e A116371 a(18) = #{10+8x1, 18x1} = 2;
%e A116371 a(19) = #{19, 10+9x1, 19x1} = 3;
%e A116371 a(20) = #{19+1, 10+10, 10+10x1, 19x1} = 4.
%o A116371 (Haskell)
%o A116371 a116371 n = p a017173_list n where
%o A116371    p _  0 = 1
%o A116371    p [] _ = 0
%o A116371    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o A116371 -- _Reinhard Zumkeller_, Feb 04 2014
%Y A116371 Cf. A010888.
%Y A116371 A147706. [From _Reinhard Zumkeller_, Nov 11 2008]
%Y A116371 A017173, A156144, A156145. [From _Reinhard Zumkeller_, Feb 05 2009]
%K A116371 nonn,base
%O A116371 1,10
%A A116371 _Reinhard Zumkeller_, Feb 12 2006