This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A128174 Transform, (1,0,1,...) in every column. 58
 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Inverse of the triangle = a tridiagonal matrix with (1,1,1,...) in the superdiagonal, (0,0,0,...) in the main diagonal and (-1,-1,-1,...) in the subdiagonal. Riordan array (1/(1-x^2), x) with inverse (1-x^2,x). - Paul Barry, Sep 10 2008 The position of 1's in this sequence is equivalent to A246705, and the position of 0's is equivalent to A246706. - Bernard Schott, Jun 05 2019 LINKS G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened FORMULA A lower triangular matrix transform, (1, 0, 1, ...) in every column; n terms of (1, 0, 1, ...) in odd rows; n terms of (0, 1, 0, ...) in even rows. T(n,k) = [k<=n]*(1+(-1)^(n-k))/2. - Paul Barry, Sep 10 2008 With offset n=1, k=0: Sum_{k=0..n} {T(n,k)*x^k} = A000035(n), A004526(n+1), A000975(n), A033113(n), A033114(n), A033115(n), A033116(n), A033117(n), A033118(n), A033119(n), A056830(n+1) for x=0,1,2,3,4,5,6,7,8,9,10 respectively. - Philippe Deléham, Oct 17 2011 T(n+1,1) = 1 - T(n,1); T(n+1,k) = T(n,k-1), 1 < k <= n+1. - Reinhard Zumkeller, Aug 01 2014 EXAMPLE First few rows of the triangle are:   1;   0, 1;   1, 0, 1;   0, 1, 0, 1;   1, 0, 1, 0, 1; ... MAPLE A128174 := proc(n, k)     if k > n or k < 1 then         0;     else         modp(k+n+1, 2) ;     end if; end proc: # R. J. Mathar, Aug 06 2016 MATHEMATICA a128174[r_] := Table[If[EvenQ[n+k], 1, 0], {n, 1, r}, {k, 1, n}] TableForm[a128174[5]] (* triangle *) Flatten[a128174[10]] (* data *) (* Hartmut F. W. Hoft, Mar 15 2017 *) Table[(1+(-1)^(n-k))/2, {n, 1, 12}, {k, 1, n}]//Flatten (* G. C. Greubel, Sep 26 2017 *) PROG (Haskell) a128174 n k = a128174_tabl !! (n-1) !! (k-1) a128174_row n = a128174_tabl !! (n-1) a128174_tabl = iterate (\xs@(x:_) -> (1 - x) : xs) [1] -- Reinhard Zumkeller, Aug 01 2014 (PARI) for(n=1, 12, for(k=1, n, print1((1+(-1)^(n-k))/2, ", "))) \\ G. C. Greubel, Sep 26 2017 (MAGMA) [[(1+(-1)^(n-k))/2: k in [1..n]]: n in [1..12]]; // G. C. Greubel, Jun 05 2019 (Sage) [[(1+(-1)^(n-k))/2 for k in (1..n)] for n in (1..12)] # G. C. Greubel, Jun 05 2019 CROSSREFS Cf. A004526 (row sums). Sequence in context: A024711 A286990 A249866 * A096055 A260456 A125144 Adjacent sequences:  A128171 A128172 A128173 * A128175 A128176 A128177 KEYWORD nonn,easy,tabl,changed AUTHOR Gary W. Adamson, Feb 17 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)