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A103633
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Triangle read by rows: triangle of repeated stepped binomial coefficients.
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2
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1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 15
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,14
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COMMENTS
| Row sums are sum{k=0..n, binomial(floor(n/2),n-k)}=(1,1,2,2,4,4,...). Diagonal sums have g.f. (1+x^2)/(1-x^3-x^4) (see A079398). Matrix inverse of the signed triangle (-1)^(n-k)T(n,k) is A103631. Matrix inverse of T(n,k) is the alternating signed version of A103631.
Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ....] DELTA [1, 0, -1, 0, 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
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FORMULA
| Number triangle T(n, k)=binomial(floor(n/2), n-k)
Sum_{n, n>=0} T(n, k) = A000045(k+2) = Fib(k+2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 08 2005
Sum_{k, 0<=k<=n}T(n,k)=2^[n/2]=A016116(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2006
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EXAMPLE
| Rows begin {1}, {0,1}, {0,1,1}, {0,0,1,1}, {0,0,0,1,2,1},...
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CROSSREFS
| Sequence in context: A064662 A024944 A117907 * A026821 A039964 A035172
Adjacent sequences: A103630 A103631 A103632 * A103634 A103635 A103636
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 11 2005
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