A034850 Triangular array formed by taking every other term of Pascal's triangle.

1, 1, 2, 1, 3, 1, 6, 1, 5, 10, 1, 6, 20, 6, 1, 21, 35, 7, 1, 28, 70, 28, 1, 9, 84, 126, 36, 1, 10, 120, 252, 120, 10, 1, 55, 330, 462, 165, 11, 1, 66, 495, 924, 495, 66, 1, 13, 286, 1287, 1716, 715, 78, 1, 14, 364, 2002, 3432, 2002, 364, 14, 1, 105, 1365, 5005, 6435

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

D. Dumont and J. Zeng, Polynômes d'Euler et les fractions continues de Stieltjes-Rogers, preprint 1996.

D. Dumont and J. Zeng, Polynômes d'Euler et les fractions continues de Stieltjes-Rogers, Ramanujan J. 2 (1998) 3, 387-410.

Formula

a(n) = A007318(2n) if both are regarded as integer sequences. - Michael Somos, Feb 11 2004

Example

Triangle begins:
  1;
  1;
  2;
  1,  3;
  1,  6,  1;
  5, 10,  1;
  6, 20,  6;
  1, 21, 35,  7;

Mathematica

Table[If[k < 0 || k > (Floor[n/4] + Floor[(n + 1)/4]), 0, Binomial[n, 2*k + Mod[Floor[(n + 1)/2], 2]]], {n, 0, 20}, {k, 0, (Floor[n/4] + Floor[(n + 1)/4])}] // Flatten (* G. C. Greubel, Feb 23 2018 *)

Prog

(PARI) {T(n, k) = if( k<0 || k>n\4 + (n+1)\4, 0, binomial(n, 2*k + (n+1)\2%2))}; /* Michael Somos, Feb 11 2004 */

Crossrefs

Cf. A007318, A034839.

Sequence in context: A377510 A084419 A119606 * A220377 A329696 A145969

Adjacent sequences: A034847 A034848 A034849 * A034851 A034852 A034853

Keyword

nonn,easy,tabf

Author

N. J. A. Sloane

Status

approved