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A244230
a(n) is the least k such that A197433(k) >= n.
7
0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 24, 24, 24, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 32, 32, 32
OFFSET
0,3
COMMENTS
For n >= 1, a(n) is the total number of ways the natural numbers in range 1 .. n can be represented as sums of distinct Catalan numbers (A000108). Note that for any one number, number of such solutions may be at most one. In other words, this sequence is one less than the partial sums of A176137 (number of partitions of n into distinct Catalan numbers).
LINKS
FORMULA
For all n >= 0, a(A197433(n)) = n. [This works as an inverse function for the injection A197433].
MATHEMATICA
nmax = 68;
A197433[n_] := If[n == 0, 0, SeriesCoefficient[(1/(1-x))*Sum[ CatalanNumber[k+1]*x^(2^k)/(1+x^(2^k)), {k, 0, Log[2, n] // Ceiling}], {x, 0, n}]];
a[n_] := For[k = 0, True, k++, If[A197433[k] >= n, Return[k]]];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Nov 18 2021, after Ilya Gutkovskiy in A197433 *)
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(define A244230 (LEAST-GTE-I 0 0 A197433))
CROSSREFS
The first differences give A176137 from its term a(1) onward.
Sequence in context: A367193 A277425 A245335 * A277814 A006162 A036701
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 25 2014
STATUS
approved