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A244224
a(n) = Number of nonnegative integers 0 <= k <= n, which have an even representation in Greedy Catalan Base (A014418).
4
1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 42
OFFSET
0,3
COMMENTS
The terms a(0) .. a(23) are equal to A076905(1) .. A076905(24).
LINKS
EXAMPLE
The first nonnegative integers represented in Greedy Catalan Base look like this:
A014418(0) = 0
A014418(1) = 1
A014418(2) = 10
A014418(3) = 11
A014418(4) = 20
A014418(5) = 100
A014418(6) = 101
A014418(7) = 110
Of these, the first "even" representation (ending with zero) occurs at n=0, thus a(0) = 1, and as 1 is odd, also a(1) = 1. The next even occurs at n=2, so a(2) = 2. The next even representations after that occur at n=4, 5 and 7, thus a(3) = 2, a(4) = 3, a(5) = 4, a(6) = 4 and a(7) = 5.
PROG
(Scheme, with Antti Karttunen's IntSeq-library for memoizing definec-macro)
(definec (A244224 n) (if (zero? n) 1 (+ (A244220 n) (A244224 (- n 1)))))
CROSSREFS
Partial sums of A244220.
One more than A244229.
Sequence in context: A317137 A139327 A076905 * A259549 A098295 A074840
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 23 2014
STATUS
approved