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 A097806 Riordan array (1+x, 1) read by rows. 46
 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. 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 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 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..10010 (Rows 0 <= n <= 140) Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012. FORMULA T(n, k) = if(n=k or n-k=1, 1, 0). a(n) = A103451(n+1). - Philippe Deléham, Oct 16 2007 From Boris Putievskiy, Jan 17 2013: (Start) a(n) = floor((A002260(n)+2)/(A003056(n)+2)), n > 0. a(n) = floor((i+2)/(t+2)), n > 0, where i=n-t*(t+1)/2, t=floor((-1+sqrt(8*n-7))/2). (End) G.f.: (1+x)/(1-x*y). - R. J. Mathar, Aug 11 2015 EXAMPLE Rows begin {1}, {1,1}, {0,1,1}, {0,0,1,1}... From Boris Putievskiy, Jan 17 2013: (Start) The start of the sequence as table: 1..1..0..0..0..0..0... 1..1..0..0..0..0..0... 1..1..0..0..0..0..0... 1..1..0..0..0..0..0... 1..1..0..0..0..0..0... 1..1..0..0..0..0..0... 1..1..0..0..0..0..0... . . . The start of the sequence as triangle array read by rows:   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, 1, 1; . . . Row number r (r>4) contains (r-2) times '0' and 2 times '1'. (End) MAPLE A097806 := proc(n, k)     if k =n or k=n-1 then         1;     else         0;     end if; end proc: # R. J. Mathar, Jun 20 2015 MATHEMATICA Table[Boole[n <= # <= n+1] & /@ Range[n+1], {n, 0, 15}] // Flatten (* or *) Table[Floor[(# +2)/(n+2)] & /@ Range[n+1], {n, 0, 15}] // Flatten (* Michael De Vlieger, Jul 21 2016 *) PROG (PARI) T(n, k) = if(k==n || k==n-1, 1, 0); \\ G. C. Greubel, Jul 11 2019 (MAGMA) [k eq n or k eq n-1 select 1 else 0: k in [0..n], n in [0..15]]; // G. C. Greubel, Jul 11 2019 (Sage) def T(n, k):     if (k==n or k==n-1): return 1     else: return 0 [[T(n, k) for k in (0..n)] for n in (0..15)] # G. C. Greubel, Jul 11 2019 CROSSREFS Sequence in context: A265695 A116938 A105589 * A167374 A294821 A132971 Adjacent sequences:  A097803 A097804 A097805 * A097807 A097808 A097809 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Aug 25 2004 STATUS approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)