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

0,4

Comments

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

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

Table of n, a(n) for n=0..54.

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.

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).

Example

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

Crossrefs

Cf. A097724.

Sequence in context: A305538 A370527 A193924 * A327917 A065602 A237596

Adjacent sequences: A110436 A110437 A110438 * A110440 A110441 A110442

Keyword

easy,nonn,tabl

Author

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

Status

approved