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

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
            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

Crossrefs

Cf. A339495 (row sums), A333650, A030528, A023531.

Sequence in context: A277448 A177760 A329440 * A104731 A240192 A264751

Adjacent sequences: A339491 A339492 A339493 * A339495 A339496 A339497

Keyword

nonn,tabl

Author

Peter Luschny, Dec 07 2020

Status

approved