A080233 Triangle T(n,k) obtained by taking differences of consecutive pairs of row elements of Pascal's triangle A007318.

1, 1, 0, 1, 1, -1, 1, 2, 0, -2, 1, 3, 2, -2, -3, 1, 4, 5, 0, -5, -4, 1, 5, 9, 5, -5, -9, -5, 1, 6, 14, 14, 0, -14, -14, -6, 1, 7, 20, 28, 14, -14, -28, -20, -7, 1, 8, 27, 48, 42, 0, -42, -48, -27, -8

Offset

0,8

Comments

Row sums are 1,1,1,1,1,1 with g.f. 1/(1-x). Can also be obtained from triangle A080232 by taking sums of pairs of consecutive row elements.

Mirror image of triangle in A156644. - Philippe Deléham, Feb 14 2009

Links

Table of n, a(n) for n=0..54.

Formula

T(n, k) = if(k>n, 0, binomial(n, k)-binomial(n, k-1)).

Example

Rows are {1}, {1,0}, {1,1,-1}, {1,2,0,-2}, {1,3,2,-2,-3}, ...

Mathematica

Table[Binomial[n, k] - Binomial[n, k - 1], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)

Prog

(PARI) {T(n, k) = if( n<0 || k>n, 0, binomial(n, k) - binomial(n, k-1))}; /* Michael Somos, Nov 25 2016 */

Crossrefs

Cf. A007318, A080232.

Sequence in context: A339374 A265753 A138110 * A156644 A097808 A349463

Adjacent sequences: A080230 A080231 A080232 * A080234 A080235 A080236

Keyword

easy,sign,tabl

Author

Paul Barry, Feb 10 2003

Status

approved