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
Examples
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.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..15000 (first 1250 terms from Reinhard Zumkeller)
Programs
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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 -
Mathematica
Length[IntegerPartitions[#,All,DeleteDuplicates@DeleteCases[IntegerDigits[#],0]]]&/@Range[200] (* Sander G. Huisman, Nov 14 2022 *)
Extensions
More terms from David Wasserman, Jul 29 2002
Comments