

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
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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(mc,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 rightshifted (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



