OFFSET
0,2
LINKS
G. C. Greubel, Rows n = 0..100 of the triangle, flattened
FORMULA
T(n, k) = 2*A132749(n, k) - 1, an infinite lower triangular matrix.
From G. C. Greubel, Feb 16 2021: (Start)
T(n, k) = A109128(n, k) with T(n, 0) = 3.
Sum_{k=0..n} T(n, k) = 2^(n+1) -n +1 -2*[n=0] = A132753(n) - 2*[n=0]. (End)
EXAMPLE
First few rows of the triangle are:
1;
3, 1;
3, 3, 1;
3, 5, 5, 1;
3, 7, 11, 7, 1;
3, 9, 19, 19, 9, 1;
3, 11, 29, 39, 29, 11, 1;
...
MATHEMATICA
T[n_, k_]:= If[k==n, 1, If[k==0, 3, 2*Binomial[n, k] -1 ]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 16 2021 *)
PROG
(Sage)
def A132752(n, k): return 1 if k==n else 3 if k==0 else 2*binomial(n, k) -1
flatten([[A132752(n, k) for k in [0..n]] for n in [0..12]]) # G. C. Greubel, Feb 16 2021
(Magma)
A132752:= func< n, k | k eq n select 1 else k eq 0 select 3 else 2*Binomial(n, k) -1 >;
[A132752(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 16 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Aug 28 2007
STATUS
approved