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A316675 Triangle read by rows: T(n,k) gives the number of ways to stack n triangles in a valley so that the right wall has k triangles for n >= 0 and 0 <= k <= n. 7
1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 3, 2, 1, 1, 1, 0, 0, 1, 1, 3, 3, 2, 1, 1, 1, 0, 0, 1, 1, 3, 3, 3, 2, 1, 1, 1, 0, 0, 1, 1, 4, 3, 4, 3, 2, 1, 1, 1, 0, 0, 1, 1, 5, 4, 5, 4, 3, 2, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,33

LINKS

Seiichi Manyama, Rows n = 0..50, flattened

FORMULA

For m >= 0,

Sum_{n>=2m}   T(n,2m)  *x^n = x^(2m)   * Product_{j=1..m} (1+x^(2j-1))/(1-x^(2j)).

Sum_{n>=2m+1} T(n,2m+1)*x^n = x^(2m+1) * Product_{j=1..m} (1+x^(2j-1))/(1-x^(2j)).

EXAMPLE

T(8,4) = 3.

    *                             *

   / \                           / \

  *---*   *     *---*---*       *---*

   \ / \ / \     \ / \ / \     / \ / \

    *---*---*     *---*---*   *---*---*

     \ / \ /       \ / \ /     \ / \ /

      *---*         *---*       *---*

       \ /           \ /         \ /

        *             *           *

Triangle begins:

1;

0, 1;

0, 0, 1;

0, 0, 1, 1;

0, 0, 1, 1, 1;

0, 0, 1, 1, 1, 1;

0, 0, 1, 1, 1, 1,  1;

0, 0, 1, 1, 2, 1,  1,  1;

0, 0, 1, 1, 3, 2,  1,  1,  1;

0, 0, 1, 1, 3, 3,  2,  1,  1,  1;

0, 0, 1, 1, 3, 3,  3,  2,  1,  1,  1;

0, 0, 1, 1, 4, 3,  4,  3,  2,  1,  1, 1;

0, 0, 1, 1, 5, 4,  5,  4,  3,  2,  1, 1, 1;

0, 0, 1, 1, 5, 5,  6,  5,  4,  3,  2, 1, 1, 1;

0, 0, 1, 1, 5, 5,  8,  6,  5,  4,  3, 2, 1, 1, 1;

0, 0, 1, 1, 6, 5, 10,  8,  7,  5,  4, 3, 2, 1, 1, 1;

0, 0, 1, 1, 7, 6, 11, 10, 10,  7,  5, 4, 3, 2, 1, 1, 1;

0, 0, 1, 1, 7, 7, 13, 11, 12, 10,  7, 5, 4, 3, 2, 1, 1, 1;

0, 0, 1, 1, 7, 7, 16, 13, 14, 12, 10, 7, 5, 4, 3, 2, 1, 1, 1;

CROSSREFS

Row sums give A006950.

Sums of even columns give A059777.

Cf. A004525, A000933, A089597, A014670, A316718, A316719, A316720, A316721, A316722.

Cf. A072233.

Sequence in context: A086831 A191340 A211229 * A111405 A089053 A214979

Adjacent sequences:  A316672 A316673 A316674 * A316676 A316677 A316678

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jul 10 2018

STATUS

approved

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Last modified May 27 07:44 EDT 2019. Contains 323599 sequences. (Running on oeis4.)