A119999 Number of partitions of n into parts that occur in decimal representation as substrings of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 6, 5, 5, 4, 4, 4, 4, 2, 12, 2, 5, 8, 4, 6, 3, 5, 3, 2, 12, 7, 2, 4, 4, 8, 3, 3, 6, 2, 12, 12, 5, 2, 4, 5, 3, 8, 3, 2, 12, 7, 5, 4, 2, 3, 3, 3, 3, 2, 12, 12, 12, 7, 4, 2, 3, 4, 5, 2, 12, 7, 5, 4, 4, 3, 2, 3, 3, 2, 12, 12, 5, 12, 4, 5, 3, 2, 3, 2, 12, 7, 12, 4, 4, 7, 3

Offset: 0

Author

Reinhard Zumkeller, Jun 13 2006

Keywords

• nonn
• base
• look

Comments

A120002 = first differences; A120003 = partial sums;

see A120000 and A120001 for records and where they occur: A120000(n)=a(A120001(n)).

Examples

			a(98) = #{98, 10*9+8, 2*9+10*8} = 3;
a(99) = #{99, 11*9} = 2;
a(100) = #{100, 10*10, 9*10+10*1, 8*10+20*1, 7*10+30*1, 6*10+40*1, 5*10+50*1, 4*10+60*1, 3*10+70*1, 2*10+80*1, 10+90*1, 100*1} = 12;
a(101) = #{101, 10*10+1, 9*10+11*1, 8*10+21*1, 7*10+31*1, 6*10+41*1, 5*10+51*1, 4*10+61*1, 3*10+71*1, 2*10+81*1, 10+91*1, 101*1} = 12;
a(102) = #{102, 10*10+2, 10*10+2*1, 9*10+6*2, ...} = 298.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000041, A061827, A120004.

Programs

Haskell

import Data.List (isInfixOf)
a119999 n = p (filter ((`isInfixOf` show n) . show) [1..n]) n where
   p _  0 = 1
   p [] _ = 0
   p ks'@(k:ks) m | m < k     = 0
                  | otherwise = p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Aug 14 2011