|
|
A172281
|
|
Triangle T(n, k, q) = ceiling( binomial(n, k)*(1+q)/( (1+q)^2 + (k - floor(n/2))^2 ) ), with q = 1, read by rows.
|
|
1
|
|
|
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 5, 4, 2, 1, 1, 2, 6, 10, 6, 2, 1, 1, 2, 9, 18, 14, 6, 2, 1, 1, 2, 7, 23, 35, 23, 7, 2, 1, 1, 2, 9, 34, 63, 51, 21, 6, 1, 1, 1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,8
|
|
LINKS
|
|
|
FORMULA
|
T(n, k, q) = ceiling( binomial(n, k)*(1+q)/( (1+q)^2 + (k - floor(n/2))^2 ) ), with q = 1.
|
|
EXAMPLE
|
Triangle begins as:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 3, 2, 1;
1, 2, 5, 4, 2, 1;
1, 2, 6, 10, 6, 2, 1;
1, 2, 9, 18, 14, 6, 2, 1;
1, 2, 7, 23, 35, 23, 7, 2, 1;
1, 2, 9, 34, 63, 51, 21, 6, 1, 1;
1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1;
|
|
MATHEMATICA
|
T[n_, k_, q_]:= Ceiling[Binomial[n, k]*(q+1)/((1+q)^2 + (k - Floor[n/2])^2)];
Table[T[n, k, 1], {n, 0, 5}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 07 2021 *)
|
|
PROG
|
(Sage)
def T(n, k, q): return ceil( binomial(n, k)*(1+q)/( (1+q)^2 + (k - n//2)^2 ) )
flatten([[T(n, k, 1) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, May 07 2021
|
|
CROSSREFS
|
Cf. A172279 (q=0), this sequence (q=1).
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|