A061827 Number of partitions of n into parts which are the digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 5, 4, 4, 3, 3, 3, 3, 1, 11, 1, 4, 7, 3, 5, 2, 4, 2, 1, 11, 6, 1, 3, 3, 7, 2, 2, 5, 1, 11, 11, 4, 1, 3, 4, 2, 7, 2, 1, 11, 6, 4, 3, 1, 2, 2, 2, 2, 1, 11, 11, 11, 6, 3, 1, 2, 3, 4, 1, 11, 6, 4, 3, 3, 2, 1, 2, 2, 1, 11, 11, 4, 11, 3, 4, 2, 1, 2, 1, 11, 6, 11, 3, 3, 6, 2, 2

Offset

1,12

Comments

a(A125289(n)) = 1, a(A125290(n)) > 1.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..15000 (first 1250 terms from Reinhard Zumkeller)

Example

For n = 11, 1+1+1+1+1+1+1+1+1+1+1. so a(11) = 1. For n = 12, 2+2+2+2+2+2 = 2+2+1+1+1+1+1+1+1+1 = ...etc
a(20) = 1: the only partitions permitted use the digits 0 and 2, so there is just 1, 20 = 2+2+2... ten times.

Mathematica

Length[IntegerPartitions[#, All, DeleteDuplicates@DeleteCases[IntegerDigits[#], 0]]]&/@Range[200] (* Sander G. Huisman, Nov 14 2022 *)

Prog

(Haskell)
import Data.List (sort, nub)
import Data.Char (digitToInt)
a061827 n =
   p n (map digitToInt $ nub $ sort $ filter (/= '0') $ show n) where
      p _ []        = 0
      p 0 _         = 1
      p m ds'@(d:ds)
        | m < d     = 0
        | otherwise = p (m - d) ds' + p m ds
-- Reinhard Zumkeller, Aug 01 2011

Crossrefs

Cf. A061828, A109950, A119999, A125291, A136460, A193513.

Sequence in context: A021061 A334399 A066960 * A273841 A112407 A154195

Adjacent sequences: A061824 A061825 A061826 * A061828 A061829 A061830

Keyword

nonn,base,easy,look

Author

Amarnath Murthy, May 28 2001

Extensions

More terms from David Wasserman, Jul 29 2002

Status

approved