|
|
A132737
|
|
Triangle T(n,k) = 2*binomial(n,k) + 1, read by rows.
|
|
2
|
|
|
1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 9, 13, 9, 1, 1, 11, 21, 21, 11, 1, 1, 13, 31, 41, 31, 13, 1, 1, 15, 43, 71, 71, 43, 15, 1, 1, 17, 57, 113, 141, 113, 57, 17, 1, 1, 19, 73, 169, 253, 253, 169, 73, 19, 1, 1, 21, 91, 241, 421, 505, 421, 241, 91, 21, 1, 1, 23, 111, 331, 661, 925, 925, 661, 331, 111, 23, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
T(n, k) = 2*A132735(n, k) - 1, an infinite lower triangular matrix.
|
|
EXAMPLE
|
First few rows of the triangle are:
1;
1, 1;
1, 5, 1;
1, 7, 7, 1;
1, 9, 13, 9, 1;
1, 11, 21, 21, 11, 1;
1, 13, 31, 41, 31, 13, 1;
1, 15, 43, 71, 71, 43, 15, 1;
...
|
|
MATHEMATICA
|
T[n_, k_]:= If[k==0 || k==n, 1, 2*Binomial[n, k] +1];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 15 2021 *)
|
|
PROG
|
(Sage)
def A132737(n, k): return 1 if (k==0 or k==n) else 2*binomial(n, k) + 1
(Magma)
A132737:= func< n, k | k eq 0 or k eq n select 1 else 2*Binomial(n, k) +1 >;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|