OFFSET
0,5
COMMENTS
Row n of A049597 has a(n+1) nonzero values.
When considering the set of nested parabolas defined by -(x^2) + p*x for integer values of p, a(n) tells us how many parabolas are intersected by the line from (1,n) to (n,n). - Gregory R. Bryant, Apr 01 2013
Number of distinct perimeters for polyominoes with n square cells. - Wesley Prosser, Sep 06 2017
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = (n+2) - ceiling(sqrt(4*n)), for n > 0. - Gregory R. Bryant, Apr 01 2013
From Wesley Prosser, Sep 06 2017: (Start)
a(n) = (n+2) - A027709(n)/2.
a(n) = (n+2) - A027434(n).
a(n) = (2n+2) - A049068(n).
a(n) = (2n+3) - A080037(n).
(End)
EXAMPLE
There are three 1's, one from the natural numbers and two from A033638.
When viewed as an array the sequence begins:
0
1
1 1
2 2
3 3 4
5 5 6
7 7 8 9
10 10 11 12
13 13 14 15 16
17 17 18 19 20
21 21 22 23 24 25
26 26 27 28 29 30
...
MATHEMATICA
Table[(n + 2) - Ceiling@ Sqrt[4 n] - 2 Boole[n == 0], {n, 0, 73}] (* Michael De Vlieger, Sep 05 2017 *)
PROG
(Haskell)
a083479 n = a083479_list !! n
a083479_list = m [0..] a033638_list where
m xs'@(x:xs) ys'@(y:ys) | x <= y = x : m xs ys'
| otherwise = y : m xs' ys
-- Reinhard Zumkeller, Apr 06 2012
(Maxima)
a(n):=((n+2)-ceiling(sqrt(4*n))); /* Gregory R. Bryant, Apr 01 2013 */
(Python)
from math import isqrt
def A083479(n): return n+1-isqrt((n<<2)-1) if n else 0 # Chai Wah Wu, Jul 28 2022
(Magma) [n eq 0 select 0 else (n+2)-Ceiling(Sqrt(4*n)): n in [0..100]]; // G. C. Greubel, Feb 17 2024
(SageMath) [(n+2)-ceil(sqrt(4*n)) -2*int(n==0) for n in range(101)] # G. C. Greubel, Feb 17 2024
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Alford Arnold, Jun 08 2003
EXTENSIONS
Edited and extended by David Wasserman, Nov 16 2004
STATUS
approved