The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A133566 Triangle read by rows: (1,1,1,...) on the main diagonal and (0,1,0,1,...) on the subdiagonal. 14
 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Usually regarded as a square matrix T when combined with other matrices and column vectors. Then T * V, where V = any sequence regarded as a column vector with offset 1 is a new sequence S [called an interpolation transform] given by S(2n) = V(2n), S(2n-1) = V(2n) + V(2n-1). Example: If T * [1,2,3,...], S = [1, 2, 5, 4, 9, 6, 13, 8, 17, ...) = A114752. A133080 is identical to A133566 except that the subdiagonal = (1,0,1,0,...). A133080 * [1,2,3,...] = A114753: (1, 3, 3, 7, 5, 11, 7, 15, 9, 19, ...). Triangle T(n,k), 0 <= k <= n, read by rows given by [0,1,-1,0,0,0,0,0,0,...] DELTA [1,0,-2,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 15 2007 LINKS FORMULA Odd rows: (n-2) zeros followed by 1, 1. Even rows: (n-1) zeros followed by 1. Sum_{k=0..n} T(n,k) = A040001(n). - Philippe Deléham, Dec 15 2007 G.f.: (-1-x*y-x^2*y)*x*y/((-1+x*y)*(1+x*y)). - R. J. Mathar, Aug 11 2015 EXAMPLE First few rows of the triangle:   1;   0, 1;   0, 1, 1;   0, 0, 0, 1;   0, 0, 0, 1, 1;   0, 0, 0, 0, 0, 1;   ... MAPLE A133566 := proc(n, k)     if n = k then         1;     elif  k=n-1 and type(n, odd) then         1;     else         0 ;     end if; end proc: # R. J. Mathar, Jun 20 2015 CROSSREFS Cf. A133080, A114752, A114753, A084938, A004001. Sequence in context: A102863 A131483 A077052 * A185907 A321016 A077051 Adjacent sequences:  A133563 A133564 A133565 * A133567 A133568 A133569 KEYWORD nonn,tabl,easy AUTHOR Gary W. Adamson, Sep 16 2007 EXTENSIONS Entry revised by N. J. A. Sloane, Jun 20 2015 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 May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)