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A244160 - OEIS
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A244160
a(0)=0, and for n >= 1, a(n) = the largest k such that k-th Catalan number <= n.
11
0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6
OFFSET
0,3
COMMENTS
Apart from 0, each n occurs A000245(n) times.
For n >= 1, a(n) gives the largest k such that C(k) <= n, where C(k) stands for the k-th Catalan number, A000108(k).
LINKS
FORMULA
a(0) = 0, and for n>=1, a(n) = A081288(n)-1.
For all n>=1, A000108(a(n)) = A081290(n).
EXAMPLE
For n=1, the largest k such that C(k) <= 1 is 1, thus a(1) = 1.
For n=2, the largest k such that C(k) <= 2 is 2, thus a(2) = 2.
For n=3, the largest k such that C(k) <= 3 is 2, thus a(3) = 2.
For n=4, the largest k such that C(k) <= 4 is 2, thus a(4) = 2.
For n=5, the largest k such that C(k) <= 5 is 3, thus a(5) = 3.
MATHEMATICA
MapIndexed[ConstantArray[First@ #2 - 1, #1] &, Differences@ Array[CatalanNumber, 8, 0]] /. {} -> {0} // Flatten (* Michael De Vlieger, Jun 08 2017 *)
Join[{0}, Table[PadRight[{}, CatalanNumber[n+1]-CatalanNumber[n], n], {n, 6}]// Flatten] (* Harvey P. Dale, Aug 23 2021 *)
PROG
(Scheme) (define (A244160 n) (if (zero? n) n (- (A081288 n) 1)))
(Python)
from sympy import catalan
def a(n):
if n==0: return 0
i=1
while True:
if catalan(i)>n: break
else: i+=1
return i - 1
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 08 2017
CROSSREFS
After zero, one less than A081288.
Sequence in context: A101787 A343607 A269024 * A064099 A134021 A330558
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 23 2014
STATUS
approved