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

1,24

Comments

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

Links

Table of n, a(n) for n=1..99.

Eric Weisstein's World of Mathematics, Digital Root

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

Example

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

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

Crossrefs

Cf. A010888.

Cf. A147706.

Sequence in context: A126030 A111373 A336757 * A165766 A102082 A358434

Adjacent sequences: A116373 A116374 A116375 * A116377 A116378 A116379

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 12 2006

Status

approved