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A114099 Number of partitions of n into parts with digital root = 9. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,19

COMMENTS

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

LINKS

Table of n, a(n) for n=0..102.

Eric Weisstein's World of Mathematics, Digital Root

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]

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A010888.

A147706. [Reinhard Zumkeller, Nov 11 2008]

Sequence in context: A255365 A256505 A073346 * A028613 A245515 A024362

Adjacent sequences:  A114096 A114097 A114098 * A114100 A114101 A114102

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Feb 12 2006

STATUS

approved

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Last modified March 24 23:06 EDT 2017. Contains 284035 sequences.