

A244229


a(n) = Number of integers 0 < k <= n, which have an even representation in Greedy Catalan Base (A014418).


4



0, 0, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42
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OFFSET

0,5


COMMENTS

This works as an inverse function for the injection A244222. We have a(A244222(n)) = n for all n.
Equally, for n >= 0, a(n) = the largest k such that A244222(k) <= n.


LINKS



FORMULA



EXAMPLE

The first positive numbers in Greedy Catalan Base representation are:
Of these, the first "even" representation (ending with zero) occurs at n=2, thus a(0) = a(1) = 0, and a(2) = 1. The next even representations occur at n=4, 5 and 7, thus a(3) = 1, a(4) = 2, a(5) = 3, a(6) = 3 and a(7) = 4.


PROG

(Scheme, two alternative definitions)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



