OFFSET
0,1
LINKS
G. C. Greubel, Rows n = 0..100 of the irregular triangle, flattened
FORMULA
T(n, k) = binomial(n+3, k + 2 + floor((n+1)/2)) + 3*binomial(n+1, k + 1 + floor((n+1)/2)), for 0 <= k <= floor(n/2), n >= 0. - G. C. Greubel, Jan 06 2024
EXAMPLE
This sequence represents the following portion of A028313(n,k), with x being the elements of A028313(2*n,n):
x;
., .;
., x, .;
., ., 6, .;
., ., x, 7, .;
., ., ., 19, 8, .;
., ., ., x, 27, 9, .;
., ., ., ., 65, 36, 10, .;
., ., ., ., x, 101, 46, 11, .;
., ., ., ., ., 231, 147, 57, 12, .;
., ., ., ., ., x, 378, 204, 69, 13, .;
As an irregular triangle this sequence begins as:
6;
7;
19, 8;
27, 9;
65, 36, 10;
101, 46, 11;
231, 147, 57, 12;
378, 204, 69, 13;
840, 582, 273, 82, 14;
1422, 855, 355, 96, 15;
3102, 2277, 1210, 451, 111, 16;
5379, 3487, 1661, 562, 127, 17;
11583, 8866, 5148, 2223, 689, 144, 18;
MATHEMATICA
T[n_, k_]:= Binomial[n+3, k+2+Floor[(n+1)/2]] + 3*Binomial[n+1, k+1 + Floor[(n+1)/2]];
Table[T[n, k], {n, 0, 16}, {k, 0, Floor[n/2]}]//Flatten (* G. C. Greubel, Jan 06 2024 *)
PROG
(Magma)
A028324:= func< n, k | Binomial(n+3, k+2+Floor((n+1)/2)) + 3*Binomial(n+1, k+1+Floor((n+1)/2)) >;
[A028324(n, k): k in [0..Floor(n/2)], n in [0..16]]; // G. C. Greubel, Jan 06 2024
(SageMath)
def A028324(n, k): return binomial(n+3, k+2+(n+1)//2) + 3*binomial(n+1, k+1+((n+1)//2))
flatten([[A028324(n, k) for k in range(1+(n//2))] for n in range(17)]) # G. C. Greubel, Jan 06 2024
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
More terms from James A. Sellers
STATUS
approved