A110439 Triangular array formed by the odd-indexed Fibonacci numbers.

1, 1, 1, 3, 2, 1, 8, 5, 3, 1, 21, 14, 8, 4, 1, 55, 38, 23, 12, 5, 1, 144, 102, 65, 36, 17, 6, 1, 377, 273, 180, 106, 54, 23, 7, 1, 987, 728, 494, 304, 166, 78, 30, 8, 1, 2584, 1936, 1346, 858, 494, 251, 109, 38, 9, 1

Offset: 0

Author

Asamoah Nkwanta (nkwanta(AT)jewel.morgan.edu), Aug 09 2005

Keywords

• easy
• nonn
• tabl

Comments

The leftmost column of the array is the odd-indexed Fibonacci numbers plus leading one.

Examples

			Triangle starts:
   1;
   1,  1;
   3,  2,  1;
   8,  5,  3,  1;
  21, 14,  8,  4,  1;
		

References

• A. Nkwanta, A Riordan matrix approach to unifying a selected class of combinatorial arrays, Congressus Numerantium, 160 (2003), pp. 33-55.
• A. Nkwanta, A note on Riordan matrices, Contemporary Mathematics Series, AMS, 252 (1999), pp. 99-107.
• A. Nkwanta, Lattice paths, generating functions and the Riordan group, Ph.D. Thesis, Howard University, Washington DC 1997.

Links

• Naiomi T. Cameron and Asamoah Nkwanta, On Some (Pseudo) Involutions in the Riordan Group, Journal of Integer Sequences, Vol. 8 (2005), Article 05.3.7.

Crossrefs

Cf. A097724.

Formula

Riordan array: ((1-2z+z^2)/(1-3z+z^2), ((1-z+z^2)-sqrt(1-2z-z^2-2z^3+z^4))/2z), R(n, k). Recurrence: R(n+1, 0) = 2R(n, 0) + Sum_{j>=1} R(n-j, 0), leftmost column. For other columns: R(n+1, k) = R(n, k-1) + R(n, k) + Sum_{j>=1} R(n-j, k+j).