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Search: id:A111669
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| A111669 |
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Triangle read by rows, based on a simple Fibonacci recursion rule. |
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+0
3
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| 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 11, 7, 1, 1, 5, 26, 32, 12, 1, 1, 6, 57, 122, 92, 20, 1, 1, 7, 120, 423, 582, 252, 33, 1, 1, 8, 247, 1389, 3333, 2598, 681, 54, 1, 1, 9, 502, 4414, 18054, 24117, 11451, 1815, 88, 1, 1, 10, 1013, 13744, 94684, 210990, 172980, 49566
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Subdiagonal is A000071(n+3). Row sums of inverse are 0^n.
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FORMULA
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Number triangle T(n, k)=T(n-1, k-1)+F(k+1)*T(n-1, k) where F(n)=A000045(n); Column k has g.f. x^k/Product(1-F(j+1)x, j, 0, k).
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EXAMPLE
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Triangle begins
1....1....2....3....5....8...13....F(k+1)
1
1....1
1....2....1
1....3....4....1
1....4...11....7....1
1....5...26...32...12....1
1....6...57..122...92...20....1
For example, T(6,3)=122=26+3*32=T(5,2)+F(4)*T(5,3)
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CROSSREFS
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Cf. A111577, A111578, A111579, A008277, A039755.
Sequence in context: A137153 A063841 A137596 this_sequence A124834 A104495 A093541
Adjacent sequences: A111666 A111667 A111668 this_sequence A111670 A111671 A111672
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2005
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EXTENSIONS
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Edited by Paul Barry, Nov 14 2005
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