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A034850 Triangular array formed by taking every other term of Pascal's triangle. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

D. Dumont and J. Zeng, PolynĂ´mes 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: A022458 A084419 A119606 * A220377 A145969 A140352

Adjacent sequences:  A034847 A034848 A034849 * A034851 A034852 A034853

KEYWORD

nonn,easy,tabf

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 17 04:27 EST 2018. Contains 317275 sequences. (Running on oeis4.)