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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127749 Inverse of number triangle A(n,k) = 1/(2n+1) if k <= n <= 2k, 0 otherwise. 2
1, 0, 3, 0, -3, 5, 0, 3, -5, 7, 0, 0, 0, -7, 9, 0, -3, 5, 0, -9, 11, 0, 0, 0, 0, 0, -11, 13, 0, 3, -5, 7, 0, 0, -13, 15, 0, 0, 0, 0, 0, 0, 0, -15, 17, 0, 0, 0, -7, 9, 0, 0, 0, -17, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 21, 0, -3, 5 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjectures: row sums modulo 2 are the Fredholm-Rueppel sequence A036987; row sums of triangle modulo 2 are A111982. Row sums are A127750.

The first conjecture is equivalent to the row sums conjecture in A111967. - R. J. Mathar, Apr 21 2021

LINKS

Table of n, a(n) for n=0..68.

FORMULA

T(n,k) = (2*k+1)*A111967(n,k). - R. J. Mathar, Apr 21 2021

EXAMPLE

Triangle begins

  1;

  0,  3;

  0, -3,  5;

  0,  3, -5,  7;

  0,  0,  0, -7,  9;

  0, -3,  5,  0, -9,  11;

  0,  0,  0,  0,  0, -11,  13;

  0,  3, -5,  7,  0,   0, -13,  15;

  0,  0,  0,  0,  0,   0,   0, -15,  17;

  0,  0,  0, -7,  9,   0,   0,   0, -17,  19;

  0,  0,  0,  0,  0,   0,   0,   0,   0, -19,  21;

  0, -3,  5,  0, -9,  11,   0,   0,   0,   0, -21,  23;

  0,  0,  0,  0,  0,   0,   0,   0,   0,   0,   0, -23, 25;

Inverse of triangle

  1;

  0, 1/3;

  0, 1/5, 1/5;

  0,  0,  1/7, 1/7;

  0,  0,  1/9, 1/9,  1/9;

  0,  0,   0,  1/11, 1/11, 1/11;

  0,  0,   0,  1/13, 1/13, 1/13, 1/13;

  0,  0,   0,   0,   1/15, 1/15, 1/15, 1/15;

  0,  0,   0,   0,   1/17, 1/17, 1/17, 1/17, 1/17;

  0,  0,   0,   0,    0,   1/19, 1/19, 1/19, 1/19, 1/19;

  0,  0,   0,   0,    0,   1/21, 1/21, 1/21, 1/21, 1/21, 1/21;

MAPLE

A127749 := proc(n, k)

    option remember ;

    if k > n then

        0 ;

    elif k = n then

        2*n+1 ;

    else

        -(2*k+1)*add( procname(n, i)/(2*i+1), i=k+1..min(n, 2*k)) ;

    end if;

end proc:

seq(seq( A127749(n, k), k=0..n), n=0..20) ; # R. J. Mathar, Feb 09 2021

MATHEMATICA

nmax = 10;

A[n_, k_] := If[k <= n <= 2k, 1/(2n+1), 0];

invA = Inverse[Table[A[n, k], {n, 0, nmax}, {k, 0, nmax}]];

T[n_, k_] := invA[[n+1, k+1]];

Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Oct 05 2020 *)

CROSSREFS

Cf. A111967.

Sequence in context: A060858 A222690 A222794 * A198431 A138188 A229704

Adjacent sequences:  A127746 A127747 A127748 * A127750 A127751 A127752

KEYWORD

sign,tabl

AUTHOR

Paul Barry, Jan 28 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 5 17:25 EDT 2021. Contains 343572 sequences. (Running on oeis4.)