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Search: id:A103631
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| A103631 |
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Triangle read by rows: an invertible triangle whose row sums are F(n+1). |
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4
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| 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 2, 1, 0, 1, 1, 4, 3, 3, 1, 0, 1, 1, 5, 4, 6, 3, 1, 0, 1, 1, 6, 5, 10, 6, 4, 1, 0, 1, 1, 7, 6, 15, 10, 10, 4, 1, 0, 1, 1, 8, 7, 21, 15, 20, 10, 5, 1, 0, 1, 1, 9, 8, 28, 21, 35, 20, 15, 5, 1, 0, 1, 1, 10, 9, 36, 28, 56, 35, 35, 15, 6, 1, 0, 1, 1, 11
(list; table; graph; listen)
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OFFSET
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0,14
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COMMENT
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Triangle inverse has general term (-1)^(n-k)*binomial(floor(n/2),n-k)}. Diagonal sums are A103632.
Triangle T(n,k), 0<=k<=n, rad by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 08 2005
Row sums are Fibonacci numbers (A000045).
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FORMULA
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Number triangle T(n, k)=binomial(floor((2n-k-1)/2), n-k)
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EXAMPLE
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Rows begin {1}, {0,1}, {0,1,1}, {0,1,1,1}, {0,1,1,2,1},..
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MATHEMATICA
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A polynomial recursion which produces this triangle: p(x, n) = p(x, n - 1) + x^2*p(x, n - 2). - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
p[x, -1] = 0; p[x, 0] = 1; p[x, 1] = x; p[x, 2] = x + x^2; p[x_, n_] := p[x, n] = p[x, n - 1] + x^2*p[x, n - 2]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 27 2008
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CROSSREFS
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Cf. A103633.
Sequence in context: A137560 A131255 A133607 this_sequence A083856 A081718 A129634
Adjacent sequences: A103628 A103629 A103630 this_sequence A103632 A103633 A103634
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 11 2005
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