A381552 Triangle read by rows T(n,k) is the number of diamond coverings for a specific number of diamonds covering an odd length row of triangles.

3, 4, 4, 5, 12, 4, 6, 25, 20, 4, 7, 44, 61, 28, 4, 8, 70, 146, 113, 36, 4, 9, 104, 301, 344, 181, 44, 4, 10, 147, 560, 876, 670, 265, 52, 4, 11, 200, 966, 1968, 2035, 1156, 365, 60, 4, 12, 264, 1572, 4026, 5368, 4082, 1834, 481, 68, 4, 13, 340, 2442, 7656, 12727, 12376, 7385, 2736, 613, 76, 4, 14, 429, 3652, 13728, 27742, 33397, 25312, 12376, 3894, 761, 84, 4

Offset: 0

Author

Craig Knecht, Feb 27 2025

Keywords

• nonn
• tabl

Comments

The total number of ways the diamond can cover a single row of length(n) triangles is the Fibonacci series. This total can be subdivided into categories based on the number of covering diamonds. The number of categories increase with the length of the row providing the structure of the triangle (see illustrations in the link below).

A381555 provides additional graphics explaining the diamond coverings.

Examples

			Triangle begins:
  3;
  4,  4;
  5, 12,   4;
  6, 25,  20,   4;
  7, 44,  61,  28,  4;
  8, 70, 146, 113, 36, 4;
  ...
		

Links

• Craig Knecht, Splitting the Fibonacci numbers.
• Craig Knecht, Fibonacci Expansion.

Crossrefs

Cf. A000297, A080856, A381555.