A172281 Triangle T(n, k, q) = ceiling( binomial(n, k)*(1+q)/( (1+q)^2 + (k - floor(n/2))^2 ) ), with q = 1, read by rows.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 5, 4, 2, 1, 1, 2, 6, 10, 6, 2, 1, 1, 2, 9, 18, 14, 6, 2, 1, 1, 2, 7, 23, 35, 23, 7, 2, 1, 1, 2, 9, 34, 63, 51, 21, 6, 1, 1, 1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1

Offset

0,8

Links

G. C. Greubel, Rows n = 0..30 of the triangle, flattened

Formula

T(n, k, q) = ceiling( binomial(n, k)*(1+q)/( (1+q)^2 + (k - floor(n/2))^2 ) ), with q = 1.

Example

Triangle begins as:
  1;
  1, 1;
  1, 1, 1;
  1, 2, 2,  1;
  1, 2, 3,  2,  1;
  1, 2, 5,  4,  2,   1;
  1, 2, 6, 10,  6,   2,  1;
  1, 2, 9, 18, 14,   6,  2,  1;
  1, 2, 7, 23, 35,  23,  7,  2, 1;
  1, 2, 9, 34, 63,  51, 21,  6, 1, 1;
  1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1;

Mathematica

T[n_, k_, q_]:= Ceiling[Binomial[n, k]*(q+1)/((1+q)^2 + (k - Floor[n/2])^2)];
Table[T[n, k, 1], {n, 0, 5}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 07 2021 *)

Prog

(Sage)
def T(n, k, q): return ceil( binomial(n, k)*(1+q)/( (1+q)^2 + (k - n//2)^2 ) )
flatten([[T(n, k, 1) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, May 07 2021

Crossrefs

Cf. A172279 (q=0), this sequence (q=1).

Sequence in context: A103343 A085263 A115092 * A304945 A176298 A259575

Adjacent sequences: A172278 A172279 A172280 * A172282 A172283 A172284

Keyword

nonn,tabl,less,easy

Author

Roger L. Bagula, Jan 30 2010

Extensions

Edited by G. C. Greubel, May 07 2021

Status

approved