OFFSET
0,13
COMMENTS
Table of min(x,y), where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
Highest power of 6 that divides A036561. - Fred Daniel Kline, May 29 2012
Triangle T(n,k) read by rows: T(n,k) = min(k,n-k). - Philippe Deléham, Feb 25 2014
LINKS
Reinhard Zumkeller, Rows n=0..100 of triangle, flattened
FORMULA
a(n) = A003983(n) - 1.
G.f.: x*y/((1-x)*(1-y)*(1-x*y)). - Franklin T. Adams-Watters, Feb 06 2006
2^T(n,k) = A144464(n,k), 3^T(n,k) = A152714(n,k), 4^T(n,k) = A152716(n,k), 5^T(n,k) = A152717(n,k). - Philippe Deléham, Feb 25 2014
a(n) = (1/2)*(t - 1 - abs(t^2 - 2*n - 1)), where t = floor(sqrt(2*n+1)+1/2). - Ridouane Oudra, May 03 2019
EXAMPLE
From Philippe Deléham, Feb 25 2014: (Start)
Top left corner of table:
0 0 0 0
0 1 1 1
0 1 2 2
0 1 2 3
Triangle T(n,k) begins:
0;
0, 0;
0, 1, 0;
0, 1, 1, 0;
0, 1, 2, 1, 0;
0, 1, 2, 2, 1, 0;
0, 1, 2, 3, 2, 1, 0;
0, 1, 2, 3, 3, 2, 1, 0;
0, 1, 2, 3, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0;
... (End)
MAPLE
T := (n, k) -> if n - k < k then n - k else k fi:
for n from 0 to 9 do seq(T(n, k), k=0..n) od; # Peter Luschny, May 07 2023
MATHEMATICA
Flatten[Table[IntegerExponent[2^(n - k) 3^k, 6], {n, 0, 20}, {k, 0, n}]] (* Fred Daniel Kline, May 29 2012 *)
PROG
(Haskell)
a004197 n k = a004197_tabl !! n !! k
a004197_tabl = map a004197_row [0..]
a004197_row n = hs ++ drop (1 - n `mod` 2) (reverse hs)
where hs = [0..n `div` 2]
-- Reinhard Zumkeller, Aug 14 2011
(PARI) T(x, y)=min(x, y) \\ Charles R Greathouse IV, Feb 07 2017
CROSSREFS
Row sums give A002620. - Reinhard Zumkeller, Jul 27 2005
Positions of zero are given in A117142. - Ridouane Oudra, Apr 30 2019
KEYWORD
AUTHOR
EXTENSIONS
Mathematica program fixed by Harvey P. Dale, Nov 26 2020
Name edited by Peter Luschny, May 07 2023
STATUS
approved