A307156 - OEIS

A307156

Number triangle T(n,k) = Sum_{j=0..n-k} (-1)^j * binomial(k,3*j) * binomial(n-k,3*j).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, -3, -3, 1, 1, 1, 1, 1, 1, -9, -15, -9, 1, 1, 1, 1, 1, 1, -19, -39, -39, -19, 1, 1, 1, 1, 1, 1, -34, -79, -99, -79, -34, 1, 1, 1, 1, 1, 1, -55, -139, -199, -199, -139, -55, 1, 1, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,32

LINKS

Seiichi Manyama, Rows n = 0..139, flattened

EXAMPLE

Triangle begins:

n\k | 0 1 2 3 4 5 6 7 8

----+-------------------------------

0 | 1;

1 | 1, 1;

2 | 1, 1, 1;

3 | 1, 1, 1, 1;

4 | 1, 1, 1, 1, 1;

5 | 1, 1, 1, 1, 1, 1;

6 | 1, 1, 1, 0, 1, 1, 1;

7 | 1, 1, 1, -3, -3, 1, 1, 1;

8 | 1, 1, 1, -9, -15, -9, 1, 1, 1;

MATHEMATICA

T[n_, k_] := Sum[(-1)^j * Binomial[k, 3*j] * Binomial[n - k, 3*j], {j, 0, n - k}]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, May 20 2021 *)

CROSSREFS

Row sums give A307089.

T(2*n,n) gives A307158.

Cf. A119326, A119335, A307090.

Sequence in context: A225054 A355604 A059790 * A326057 A130778 A353516

Adjacent sequences: A307153 A307154 A307155 * A307157 A307158 A307159

KEYWORD

sign,look,tabl

AUTHOR

Seiichi Manyama, Mar 27 2019

STATUS

approved