A114099 Number of partitions of n into parts with digital root = 9.

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Feb 12 2006

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 0..19683
• Eric Weisstein's World of Mathematics, Digital Root

Crossrefs

Cf. A000041, A010888, A035444, A147706.

Programs

Mathematica

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

PARI

A114099(n) = if((n%9), 0, numbpart(n/9)); \\ Antti Karttunen, Jul 22 2018

Formula

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

a(9n) = A000041(n) and for all others a(n) = 0. [Robert G. Wilson v, Apr 25 2010]