|
%I #7 Feb 04 2014 08:58:03
%S 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,
%T 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,
%U 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
%N Number of partitions of n into parts having in decimal representation the same digital root as n has.
%C a(n) <= a(n+9); Max{n: a(n)=1} = 71;
%C A156145 and A017173 give record values and where they occur: a(A017173(n-1))=A156145(n);
%C a(A017173(n)) = A116371(A017173(n)).
%H R. Zumkeller, <a href="/A156144/b156144.txt">Table of n, a(n) for n = 1..500</a>
%e a(19) = #{19, 10+1+1+1+1+1+1+1+1+1, 19x1} = 3;
%e a(20) = #{20, 2+2+2+2+2+2+2+2+2+2} = 2;
%e a(21) = #{21, 3+3+3+3+3+3+3, 12+3+3+3} = 3;
%e a(22) = #{22} = 1;
%o (Haskell)
%o a156144 n = p [x | x <- [1..n], a010888 x == a010888 n] n where
%o p _ 0 = 1
%o p [] _ = 0
%o p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%o -- _Reinhard Zumkeller_, Feb 04 2014
%Y A010888, A114102.
%K base,nonn,look
%O 1,10
%A _Reinhard Zumkeller_, Feb 05 2009
|
