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A119999 Number of partitions of n into parts that occur in decimal representation as substrings of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A024558 A238452 A103238 * A061828 A086535 A067436

Adjacent sequences:  A119996 A119997 A119998 * A120000 A120001 A120002

KEYWORD

nonn,base,look

AUTHOR

Reinhard Zumkeller, Jun 13 2006

STATUS

approved

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Last modified July 11 04:33 EDT 2020. Contains 335609 sequences. (Running on oeis4.)