A156144 Number of partitions of n into parts having in decimal representation the same digital root as n has.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 3, 2, 3, 1, 1, 2, 1, 1, 3, 5, 2, 5, 1, 1, 2, 1, 1, 5, 8, 4, 8, 2, 1, 4, 1, 1, 7, 13, 5, 13, 2, 2, 5, 1, 1, 11, 20, 9, 19, 3, 2, 9, 1, 1, 15, 31, 12, 29, 4, 3, 11, 2, 1, 22, 46, 20, 42, 7, 4, 18, 2, 2, 30, 68, 27, 61, 9, 6, 23, 3, 2, 42, 98, 42, 85

Offset: 1

Author

Reinhard Zumkeller, Feb 05 2009

Keywords

• base
• nonn
• look

Comments

a(n) <= a(n+9); Max{n: a(n)=1} = 71;

A156145 and A017173 give record values and where they occur: a(A017173(n-1))=A156145(n);

a(A017173(n)) = A116371(A017173(n)).

Examples

			a(19) = #{19, 10+1+1+1+1+1+1+1+1+1, 19x1} = 3;
a(20) = #{20, 2+2+2+2+2+2+2+2+2+2} = 2;
a(21) = #{21, 3+3+3+3+3+3+3, 12+3+3+3} = 3;
a(22) = #{22} = 1;
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..500

Crossrefs

A010888, A114102.

Programs

Haskell

a156144 n = p [x | x <- [1..n], a010888 x == a010888 n] n where
   p _  0 = 1
   p [] _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Feb 04 2014