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A244225
a(n) = Number of nonnegative integers 0 <= k <= n, which have an odd representation in Greedy Catalan Base (A014418).
6
0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 32
OFFSET
0,4
COMMENTS
This works also as an inverse function for injection A244223: we have a(A244223(n)) = n for all n >= 1.
Equally, for n >= 1, a(n) = the largest k such that A244223(k) <= n.
After 0, each n occurs A244228(n) times.
LINKS
FORMULA
a(n) = n - A244229(n).
EXAMPLE
The first nonnegative integers represented in Greedy Catalan Base look like:
A014418(0) = 0
A014418(1) = 1
A014418(2) = 10
A014418(3) = 11
A014418(4) = 20
A014418(5) = 100
A014418(6) = 101
Of these, the first "odd" representation (ending with one) occurs at n=1, thus a(0) = 0, but a(1) = 1. As the next odd occurs at n=3, also a(2) = 1, but a(3) = 1+1 = 2. The next odd representation does not occur until at n=6, thus a(4) = a(5) = 2 and a(6) = 3.
PROG
(Scheme, with Antti Karttunen's IntSeq-library for memoizing definec-macro)
(definec (A244225 n) (if (<= n 1) n (+ (A244221 n) (A244225 (- n 1)))))
CROSSREFS
Partial sums of A244221.
Sequence in context: A172267 A231151 A097508 * A109964 A247366 A285760
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 23 2014
STATUS
approved