This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A316675 #57 Apr 06 2025 13:39:52
%S A316675 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,
%T A316675 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,
%U A316675 1,1,4,3,4,3,2,1,1,1,0,0,1,1,5,4,5,4,3,2,1,1,1
%N 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.
%H A316675 Seiichi Manyama, <a href="/A316675/b316675.txt">Rows n = 0..100, flattened</a>
%F A316675 For m >= 0,
%F A316675 Sum_{n>=2m} T(n,2m) *x^n = x^(2m) * Product_{j=1..m} (1+x^(2j-1))/(1-x^(2j)).
%F A316675 Sum_{n>=2m+1} T(n,2m+1)*x^n = x^(2m+1) * Product_{j=1..m} (1+x^(2j-1))/(1-x^(2j)).
%e A316675 T(8,4) = 3.
%e A316675 * *
%e A316675 / \ / \
%e A316675 *---* * *---*---* *---*
%e A316675 \ / \ / \ \ / \ / \ / \ / \
%e A316675 *---*---* *---*---* *---*---*
%e A316675 \ / \ / \ / \ / \ / \ /
%e A316675 *---* *---* *---*
%e A316675 \ / \ / \ /
%e A316675 * * *
%e A316675 Triangle begins:
%e A316675 1;
%e A316675 0, 1;
%e A316675 0, 0, 1;
%e A316675 0, 0, 1, 1;
%e A316675 0, 0, 1, 1, 1;
%e A316675 0, 0, 1, 1, 1, 1;
%e A316675 0, 0, 1, 1, 1, 1, 1;
%e A316675 0, 0, 1, 1, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 3, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 3, 3, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 4, 3, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 5, 4, 5, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 5, 5, 6, 5, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 5, 5, 8, 6, 5, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 6, 5, 10, 8, 7, 5, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 7, 6, 11, 10, 10, 7, 5, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 7, 7, 13, 11, 12, 10, 7, 5, 4, 3, 2, 1, 1, 1;
%e A316675 0, 0, 1, 1, 7, 7, 16, 13, 14, 12, 10, 7, 5, 4, 3, 2, 1, 1, 1;
%e A316675 ...
%Y A316675 Row sums give A006950.
%Y A316675 Sums of even columns give A059777.
%Y A316675 Cf. A004525, A000933, A089597, A014670, A316718, A316719, A316720, A316721, A316722.
%Y A316675 Cf. A072233.
%K A316675 nonn,tabl
%O A316675 0,33
%A A316675 _Seiichi Manyama_, Jul 10 2018