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A176137 Number of partitions of n into distinct Catalan numbers, cf. A000108. 11

%I

%S 1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,1,0,1,1,1,1,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Number of partitions of n into distinct Catalan numbers, cf. A000108.

%C a(n) <= 1;

%C a(A000108(n)) = 1; a(A141351(n)) = 1; a(A014138(n)) = 1.

%C A197433 gives all such numbers k that a(k) = 1, in other words, this is the characteristic function of A197433, and all three sequences mentioned above are its subsequences. - _Antti Karttunen_, Jun 25 2014

%H R. Zumkeller, <a href="/A176137/b176137.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = f(n,1,1) with f(m,k,c) = if c>m then 0^m else f(m-c,k+1,c') + f(m,k+1,c') where c'=2*c*(2*k+1)/(k+2).

%e 56 = 42+14 = A000108(5)+A000108(4), all other sums of distinct Catalan numbers are not equal 56, therefore a(56)=1.

%o (Scheme) (define (A176137 n) (if (zero? n) 1 (- (A244230 (+ n 1)) (A244230 n)))) ;; _Antti Karttunen_, Jun 25 2014

%Y When right-shifted (prepended with 1) this sequence is the first differences of A244230.

%Y Cf. A033552, A197433, A161227 - A161239.

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Apr 09 2010

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Last modified October 18 03:15 EDT 2018. Contains 316302 sequences. (Running on oeis4.)