A244224 a(n) = Number of nonnegative integers 0 <= k <= n, which have an even representation in Greedy Catalan Base (A014418).

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

Antti Karttunen, Table of n, a(n) for n = 0..4862

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.

Cf. A244225, A076905.

Sequence in context: A317137 A139327 A076905 * A259549 A098295 A074840

Adjacent sequences: A244221 A244222 A244223 * A244225 A244226 A244227

Keyword

nonn

Author

Antti Karttunen, Jun 23 2014

Status

approved