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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

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, 20}, {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, 20, for(k=1, n, print1((1 + (-1)^(n - k))/2, ", "))) \\ G. C. Greubel, Sep 26 2017

CROSSREFS

Cf. A004526 (row sums).

Sequence in context: A129686 A104974 A024711 * A096055 A125144 A115198

Adjacent sequences:  A128171 A128172 A128173 * A128175 A128176 A128177

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Feb 17 2007

STATUS

approved

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Last modified February 23 21:23 EST 2018. Contains 299588 sequences. (Running on oeis4.)