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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. A072233.
Sequence in context: A191340 A211229 A335621 * A111405 A089053 A214979
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jul 10 2018
STATUS
approved

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Last modified June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)