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

0,11

Comments

A120002 = first differences; A120003 = partial sums;

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A000041, A061827, A120004.

Sequence in context: A238452 A103238 A371937 * A061828 A086535 A344601

Adjacent sequences: A119996 A119997 A119998 * A120000 A120001 A120002

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Jun 13 2006

Status

approved