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A114099
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Number of partitions of n into parts with digital root = 9.
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11
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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; internal format)
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OFFSET
| 1,18
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COMMENTS
| a(n) = A114102(n) - A116371(n) - A116372(n) - A116373(n) - A116374(n) - A116375(n) - A116376(n) - A116377(n) - A116378(n).
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LINKS
| Eric Weisstein's World of Mathematics, Digital Root
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FORMULA
| a(n) = A000041(floor(n/9))*0^(n mod 9).
a(9n) = A000041(n) and for all others a(n) = 0. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 25 2010]
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EXAMPLE
| a(27) = #{27, 18+9, 9+9+9} = 3.
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MATHEMATICA
| f[n_] := PartitionsP[n/9] If[Mod[n, 9] == 0, 1, 0]; Array[f, 105] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 25 2010]
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CROSSREFS
| Cf. A010888.
A147706. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 11 2008]
Sequence in context: A181011 A084863 A073346 * A028613 A024362 A104488
Adjacent sequences: A114096 A114097 A114098 * A114100 A114101 A114102
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KEYWORD
| nonn,base
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 12 2006
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