A339494 - OEIS

A339494

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.

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

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..66.

Peter Luschny, Domino towers classified by the size of the base floor. Illustrating row 4 of the triangle.

EXAMPLE

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