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

0,1

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.

Links

Table of n, a(n) for n=0..77.

Craig Knecht, Splitting the Fibonacci numbers.

Craig Knecht, Fibonacci Expansion.

Example

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

Crossrefs

Cf. A000297, A080856, A381555.

Sequence in context: A059179 A384318 A279678 * A222283 A336094 A182487

Adjacent sequences: A381549 A381550 A381551 * A381553 A381554 A381555

Keyword

nonn,tabl

Author

Craig Knecht, Feb 27 2025

Status

approved