A116376 Number of partitions of n into parts with digital root = 6.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 3, 0, 0, 2, 0, 0, 3, 0, 0, 3, 0, 0, 4, 0, 0, 4, 0, 0, 6, 0, 0, 5, 0, 0, 7, 0, 0, 7, 0, 0, 9, 0, 0, 9, 0, 0, 12, 0, 0, 11, 0, 0, 15, 0, 0, 15, 0, 0, 18, 0, 0, 19, 0, 0, 23, 0, 0, 23, 0, 0, 29, 0, 0, 29, 0, 0, 35, 0, 0, 37

Offset: 1

Author

Reinhard Zumkeller, Feb 12 2006

Keywords

• nonn
• base

Comments

a(n) = A114102(n) - A116371(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116377(n) - A116378(n) - A114099(n).

Examples

			a(30) = #{24+6, 15+15, 6+6+6+6+6} = 3.
		

Links

• Eric Weisstein's World of Mathematics, Digital Root

Crossrefs

Cf. A010888.

Cf. A147706.

Programs

Maple

N:= 1000: # to get a(1) to a(N)
g:= mul(1/(1-x^(6+9*j)), j=0..floor((N-6)/9)):
S:= series(g, x, N+1):
seq(coeff(S,x,j),j=1..N); # Robert Israel, Apr 13 2015

Formula

a(n) = A035386(floor(n/3))*0^(n mod 3).

G.f.: Product_{j>=0} 1/(1 - x^(6+9*j)). - Robert Israel, Apr 13 2015