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A339494
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T(n, k) is the number of domino towers of n bricks with height at most 3 and k bricks in the base floor. Triangle read by rows, T(n, k) for 1 <= k <= n.
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4
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1, 2, 1, 5, 3, 1, 5, 9, 4, 1, 3, 14, 14, 5, 1, 1, 16, 29, 20, 6, 1, 0, 12, 46, 51, 27, 7, 1, 0, 5, 52, 101, 81, 35, 8, 1, 0, 1, 41, 150, 190, 120, 44, 9, 1, 0, 0, 22, 169, 345, 323, 169, 54, 10, 1, 0, 0, 7, 143, 495, 687, 511, 229, 65, 11, 1
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OFFSET
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1,2
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COMMENTS
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This is the third triangle in a sequence of triangles: The first is the unit triangle A023531; the second is the binomial triangle C(k, n-k) without the first column, triangle A030528. This triangle highlights the connection between the Pascal triangle and the Fibonacci numbers in the case m = 2. Similarly, the current triangle and its row sums generalizes this to the case m = 3 of the construction of Union(A333650(n, j), j=1..m), classified by the number of bricks in the base floor.
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LINKS
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EXAMPLE
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Triangle starts: n: [row] sum
1: [1] 1
2: [2, 1] 3
3: [5, 3, 1] 9
4: [5, 9, 4, 1] 19
5: [3, 14, 14, 5, 1] 37
6: [1, 16, 29, 20, 6, 1] 73
7: [0, 12, 46, 51, 27, 7, 1] 144
8: [0, 5, 52, 101, 81, 35, 8, 1] 283
9: [0, 1, 41, 150, 190, 120, 44, 9, 1] 556
10: [0, 0, 22, 169, 345, 323, 169, 54, 10, 1] 1093
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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