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Search: id:A110439
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| A110439 |
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Triangular array formed by the odd indexed Fibonacci numbers. |
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+0
1
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| 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
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The leftmost column of the array is the odd indexed Fibonacci numbers plus leading one.
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REFERENCES
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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.
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.
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FORMULA
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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(R(n-j, 0))j>=1, leftmost column. For other columns: R(n+1, k) = R(n, k-1)+ R(n, k) + sum(R(n-j, k+j))j>=1.
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EXAMPLE
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Triangle starts:
1;
1,1;
3,2,1;
8,5,3,1;
21,14,8,4,1;
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CROSSREFS
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Cf. A097724.
Sequence in context: A143774 A158474 A090452 this_sequence A065602 A016648 A104552
Adjacent sequences: A110436 A110437 A110438 this_sequence A110440 A110441 A110442
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Asamoah Nkwanta (nkwanta(AT)jewel.morgan.edu), Aug 09 2005
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