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(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

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base,nonn,look

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_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Feb 05 2009

R. Zumkeller, <a href="/A156144/b156144.txt">Table of n, a(n) for n = 1..500</a>

base,nonn,new

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

1,10

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)).

R. Zumkeller, <a href="b156144.txt">Table of n, a(n) for n = 1..500</a>

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;

A010888, A114102.

base,nonn,new

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 05 2009

approved