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A097806 Riordan array (1+x,1) read by rows. 45

%I

%S 1,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,

%T 1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,

%U 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1

%N Riordan array (1+x,1) read by rows.

%C Pair sum operator. Columns have g.f. (1+x)x^k. Row sums are A040000. Diagonal sums are (1,1,1,....). Riordan inverse is (1/(1+x), 1). A097806=B*A059260^(-1), where B is the binomial matrix.

%C Triangle T(n,k), 0<=k<=n, read by rows given by [1, -1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - _Philippe Deléham_, May 01 2007

%C Table T(n,k) read by antidiagonals. T(n,1) = 1, T(n,2) = 1, T(n,k) = 0, k > 2. - Boris Putievskiy, Jan 17 2013

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [of] Integer Sequences And Pairing Functions</a> arXiv:1212.2732 [math.CO].

%F Number triangle T(n, k)=if(n=k or n-k=1, 1, 0).

%F a(n)=A103451(n+1). - _Philippe Deléham_, Oct 16 2007

%F From _Boris Putievskiy_, Jan 17 2013: (Start)

%F a(n) = floor((A002260(n)+2)/(A003056(n)+2)), n > 0.

%F a(n) = floor((i+2)/(t+2)), n > 0,

%F where i=n-t*(t+1)/2, t=floor((-1+sqrt(8*n-7))/2). (End)

%e Rows begin {1}, {1,1}, {0,1,1}, {0,0,1,1}...

%e From _Boris Putievskiy_, Jan 17 2013: (Start)

%e The start of the sequence as table:

%e 1..1..0..0..0..0..0...

%e 1..1..0..0..0..0..0...

%e 1..1..0..0..0..0..0...

%e 1..1..0..0..0..0..0...

%e 1..1..0..0..0..0..0...

%e 1..1..0..0..0..0..0...

%e 1..1..0..0..0..0..0...

%e . . .

%e The start of the sequence as triangle array read by rows:

%e 1;

%e 1,1;

%e 0,1,1;

%e 0,0,1,1;

%e 0,0,0,1,1;

%e 0,0,0,0,1,1;

%e 0,0,0,0,0,1,1;

%e 0,0,0,0,0,0,1,1;

%e . . .

%e Row number r (r>4) contains (r-2) times '0' and 2 times '1'. (End)

%K easy,nonn,tabl

%O 0,1

%A _Paul Barry_, Aug 25 2004

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Last modified December 18 16:39 EST 2014. Contains 252168 sequences.