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

Author

Mohammad K. Azarian

Keywords

• nonn
• tabf

Examples

			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;
		

Links

• G. C. Greubel, Rows n = 0..100 of the irregular triangle, flattened

Crossrefs

Cf. A028313, A028323.

Programs

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

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 *)

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

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

Extensions

More terms from James Sellers