A114099 - OEIS

%I #14 Jul 22 2018 08:48:18

%S 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,

%T 0,0,5,0,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,0,11,0,0,0,0,0,0,0,0,15,0,0,0,

%U 0,0,0,0,0,22,0,0,0,0,0,0,0,0,30,0,0,0,0,0,0,0,0,42,0,0,0,0,0,0,0,0,56,0,0,0

%N Number of partitions of n into parts with digital root = 9.

%C a(n) = A114102(n) - A116371(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116376(n) - A116377(n) - A116378(n).

%H Antti Karttunen, <a href="/A114099/b114099.txt">Table of n, a(n) for n = 0..19683</a>

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

%F a(n) = A000041(floor(n/9))*0^(n mod 9).

%F a(9n) = A000041(n) and for all others a(n) = 0. [_Robert G. Wilson v_, Apr 25 2010]

%e a(27) = #{27, 18+9, 9+9+9} = 3.

%t f[n_] := PartitionsP[n/9] If[Mod[n, 9] == 0, 1, 0]; Array[f, 105] (* _Robert G. Wilson v_, Apr 25 2010 *)

%o (PARI) A114099(n) = if((n%9), 0, numbpart(n/9)); \\ _Antti Karttunen_, Jul 22 2018

%Y Cf. A000041, A010888, A035444, A147706.

%K nonn,base

%O 0,19

%A _Reinhard Zumkeller_, Feb 12 2006