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A061827 Number of partitions of n into parts which are the digits of n. 9

%I

%S 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,

%T 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,

%U 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

%N Number of partitions of n into parts which are the digits of n.

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

%H Reinhard Zumkeller and Alois P. Heinz, <a href="/A061827/b061827.txt">Table of n, a(n) for n = 1..15000</a> [Terms 1 through 1250 were computed by _Reinhard Zumkeller_, terms 1251 through 15000 by _Alois P. Heinz_]

%e 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

%e a(20) = 1: the only partitions permitted use the digits 0 and 2, so there is just 1, 20 = 2+2+2... ten times.

%o (Haskell)

%o import Data.List (sort, nub)

%o import Data.Char (digitToInt)

%o a061827 n =

%o p n (map digitToInt $ nub $ sort $ filter (/= '0') $ show n) where

%o p _ [] = 0

%o p 0 _ = 1

%o p m ds'@(d:ds)

%o | m < d = 0

%o | otherwise = p (m - d) ds' + p m ds

%o -- _Reinhard Zumkeller_, Aug 01 2011

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

%K nonn,base,easy,look

%O 1,12

%A _Amarnath Murthy_, May 28 2001

%E More terms from _David Wasserman_, Jul 29 2002

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Last modified June 25 03:09 EDT 2021. Contains 345449 sequences. (Running on oeis4.)