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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 * A290808 A190239 A120529

Adjacent sequences:  A176134 A176135 A176136 * A176138 A176139 A176140

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 09 2010

STATUS

approved

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Last modified May 21 18:56 EDT 2019. Contains 323444 sequences. (Running on oeis4.)