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A110439
Triangular array formed by the odd-indexed Fibonacci numbers.
0
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
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
KEYWORD
easy,nonn,tabl
AUTHOR
Asamoah Nkwanta (nkwanta(AT)jewel.morgan.edu), Aug 09 2005
STATUS
approved