A028324 Elements to the right of the central elements of the 5-Pascal triangle A028313 that are not 1.

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, 20449, 14014, 7371, 2912, 833

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

Cf. A028313, A028323.

Sequence in context: A301313 A005302 A367599 * A074342 A329072 A102789

Adjacent sequences: A028321 A028322 A028323 * A028325 A028326 A028327

Keyword

nonn,tabf

Author

Mohammad K. Azarian

Extensions

More terms from James A. Sellers

Status

approved