A120001 -id:A120001 - cp's OEIS frontend

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

Reinhard Zumkeller, Jun 13 2006

A120002 = first differences; A120003 = partial sums;

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

			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.

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

Cf. A000041, A061827, A120004.

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

A120000 Record values in A119999.

Original entry on oeis.org

1, 2, 8, 12, 298, 1230, 10494, 74543, 238174, 402385, 608924, 858896, 1150972, 1486709, 1864309, 2285798, 91850628, 4005374676, 4028841935, 69750785781, 88657850823, 95628273398, 154486668208, 3487100060522, 49842735693373, 263064249410400, 751941667877632, 1790364658467926, 3748860728854527

Offset: 1

Reinhard Zumkeller, Jun 13 2006

a(n)=A119999(A120001(n)) and A119999(m)A120001(n).

			21 is where a record occurs in A119999 and A119999(21) = 12 so 12 is a record value of A119999. - _David A. Corneth_, Sep 07 2022

David A. Corneth, Table of n, a(n) for n = 1..51

Corrected by T. D. Noe, Oct 25 2006

More terms from David A. Corneth, Sep 07 2022

cp's OEIS Frontend

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

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