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 A176137 Number of partitions of n into distinct Catalan numbers, cf. A000108. 11
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) <= 1; a(A000108(n)) = 1; a(A141351(n)) = 1; a(A014138(n)) = 1. 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 LINKS R. Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA 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). EXAMPLE 56 = 42+14 = A000108(5)+A000108(4), all other sums of distinct Catalan numbers are not equal 56, therefore a(56)=1. PROG (Scheme) (define (A176137 n) (if (zero? n) 1 (- (A244230 (+ n 1)) (A244230 n)))) ;; Antti Karttunen, Jun 25 2014 CROSSREFS When right-shifted (prepended with 1) this sequence is the first differences of A244230. Cf. A033552, A197433, A161227 - A161239. Sequence in context: A071022 A155076 A257196 * A120529 A099443 A132342 Adjacent sequences:  A176134 A176135 A176136 * A176138 A176139 A176140 KEYWORD nonn AUTHOR Reinhard Zumkeller, Apr 09 2010 STATUS approved

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