This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114099 #15 Feb 16 2025 08:32:59
%S A114099 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 A114099 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 A114099 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 A114099 Number of partitions of n into parts with digital root = 9.
%C A114099 a(n) = A114102(n) - A116371(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116376(n) - A116377(n) - A116378(n).
%H A114099 Antti Karttunen, <a href="/A114099/b114099.txt">Table of n, a(n) for n = 0..19683</a>
%H A114099 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>
%F A114099 a(n) = A000041(floor(n/9))*0^(n mod 9).
%F A114099 a(9n) = A000041(n) and for all others a(n) = 0. [_Robert G. Wilson v_, Apr 25 2010]
%e A114099 a(27) = #{27, 18+9, 9+9+9} = 3.
%t A114099 f[n_] := PartitionsP[n/9] If[Mod[n, 9] == 0, 1, 0]; Array[f, 105] (* _Robert G. Wilson v_, Apr 25 2010 *)
%o A114099 (PARI) A114099(n) = if((n%9), 0, numbpart(n/9)); \\ _Antti Karttunen_, Jul 22 2018
%Y A114099 Cf. A000041, A010888, A035444, A147706.
%K A114099 nonn,base
%O A114099 0,19
%A A114099 _Reinhard Zumkeller_, Feb 12 2006