A119999 - OEIS

%I #19 Oct 28 2019 04:26:13

%S 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,

%T 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,

%U 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

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

%C A120002 = first differences; A120003 = partial sums;

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

%H Reinhard Zumkeller, <a href="/A119999/b119999.txt">Table of n, a(n) for n = 0..1000</a>

%e a(98) = #{98, 10*9+8, 2*9+10*8} = 3;

%e a(99) = #{99, 11*9} = 2;

%e 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;

%e 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;

%e a(102) = #{102, 10*10+2, 10*10+2*1, 9*10+6*2, ...} = 298.

%o (Haskell)

%o import Data.List (isInfixOf)

%o a119999 n = p (filter ((`isInfixOf` show n) . show) [1..n]) n where

%o    p _  0 = 1

%o    p [] _ = 0

%o    p ks'@(k:ks) m | m < k     = 0

%o                   | otherwise = p ks' (m - k) + p ks m

%o -- _Reinhard Zumkeller_, Aug 14 2011

%Y Cf. A000041, A061827, A120004.

%K nonn,base,look

%O 0,11

%A _Reinhard Zumkeller_, Jun 13 2006