A001003
identification: the entry's rule defines the sequence for every index; tail: the sequence is the entry's tail after some prefix rows; match_*: finite agreement only.
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A114656: Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k peaks (1 <= k <=…
(match row sums)
1 · 2, 1 · 4, 6, 1 · 8, 24, 12, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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A114687 → reverse
(match row sums)
1 · 2, 1 · 4, 6, 1 · 8, 24, 12, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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narayana → x ↦ x/(x+1)
(match row sums)
1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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A126216: Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= 1; 0 <= k <= n-1).
(match row sums)
1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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A033282: Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
(match row sums)
1 · 1, 2 · 1, 5, 5 · 1, 9, 21, 14 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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narayana → basis A007318
(match row sums)
1 · 2, 1 · 5, 5, 1 · 14, 21, 9, 1 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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A114687: Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k double rises (0 …
(match row sums)
1 · 1, 2 · 1, 6, 4 · 1, 12, 24, 8 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …
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A114656 → reverse
(match row sums)
1 · 1, 2 · 1, 6, 4 · 1, 12, 24, 8 … row sums 1, 3, 11, 45, 197, 903, 4279, 20793, …