A061828 -id:A061828 - cp's OEIS frontend

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

Amarnath Murthy, May 28 2001

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

			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.

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

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

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

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

More terms from David Wasserman, Jul 29 2002

A193513 Number of partitions of n into parts having at least one common digit in decimal representation.

Original entry on oeis.org

1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 3, 8, 5, 9, 9, 13, 9, 16, 12, 18, 16, 23, 20, 31, 30, 38, 38, 51, 49, 64, 62, 79, 77, 95, 101, 118, 118, 143, 145, 179, 181, 216, 223, 267, 286, 325, 341, 399, 416, 485, 500, 575, 600, 686, 735, 823, 864, 981, 1032, 1180

Offset: 0

Reinhard Zumkeller, Jul 30 2011

			a(7) = #{7, 7x1} = 2;
a(8) = #{8, 4+4, 2+2+2+2, 8x1} = 4;
a(9) = #{9, 3+3+3, 9x1} = 3;
a(10) = #{10, 5+5, 2+2+2+2+2, 10x1} = 4;
a(11) = #{11, 10+1, 11x1} = 3;
a(12) = #{12, 11+1, 10+1+1, 6+6, 4+4+4, 3+3+3+3, 6x2, 10x1} = 8;
a(13) = #{13, 12+1, 11+1+1, 10+1+1+1, 13x1} = 5;
a(14) = #{14, 13+1, 12+2, 12+1+1, 11+1+1+1, 10+4x1, 7+7, 7x2, 14x1} = 9.

Cf. A061827, A061828, A109950, A119999.

import Data.List (intersect)
a193513 n = p "0123456789" n 1 where
   p ""        = 0
   p   0       = 1
   p cds m k
     | m < k     = 0
     | otherwise = p (cds `intersect` show k) (m - k) k + p cds m (k + 1)

Thanks to Douglas McNeil, who noticed a program error; data corrected and program fixed by Reinhard Zumkeller, Aug 01 2011

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

Extensions