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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: A191340 A211229 A335621 * 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 June 20 03:21 EDT 2024. Contains 373512 sequences. (Running on oeis4.)