A114099 - OEIS

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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 (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	`Antti Karttunen, Table of n, a(n) for n = 0..19683` `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 *)`
	PROG	`(PARI) A114099(n) = if((n%9), 0, numbpart(n/9)); \\ Antti Karttunen, Jul 22 2018`
	CROSSREFS	`Cf. A000041, A010888, A035444, A147706.` `Sequence in context: A256505 A337196 A073346 * A028613 A318381 A341755` `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 July 19 01:33 EDT 2022. Contains 355464 sequences. (Running on oeis4.)