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A115361 Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation). 23
1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are the 'ruler function' A001511. Columns are stretched Fredholm-Rueppel sequences. Inverse is A115359.

Eigensequence of triangle A115361 = A018819 starting with offset 1: (1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, ...). [Gary W. Adamson, Nov 21 2009]

From Gary W. Adamson, Nov 27 2009: (Start)

  A115361 * [1, 2, 3, ...] = A129527 = (1, 3, 3, 7, 5, 9, 7, 15, ...)

  (A115361)^(-1) * [1, 2, 3, ...] = A115359 * [1, 2, 3, ...] = A026741 starting /Q (1, 1, 3, 2, 5, 3, 7, 4, 9, ...). (End)

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Number triangle whose k-th column has g.f. x^k*sum{j>=0} x^((2^j-1)*(k+1)).

EXAMPLE

Triangle begins:

1;

1,1;

0,0,1;

1,1,0,1;

0,0,0,0,1;

0,0,1,0,0,1;

0,0,0,0,0,0,1;

1,1,0,1,0,0,0,1;

0,0,0,0,0,0,0,0,1;

0,0,0,0,1,0,0,0,0,1;

0,0,0,0,0,0,0,0,0,0,1;

MAPLE

A115361 := proc(n, k)

    for j from 0 do

        if k+(2*j-1)*(k+1) > n then

            return 0 ;

        elif k+(2^j-1)*(k+1) = n then

            return 1 ;

        end if;

    end do;

end proc: # R. J. Mathar, Jul 14 2012

MATHEMATICA

(*recurrence*)

Clear[t]

t[1, 1] = 1;

t[n_, k_] :=

t[n, k] =

  If[k == 1, Sum[t[n, k + i], {i, 1, 2 - 1}],

   If[Mod[n, k] == 0, t[n/k, 1], 0], 0]

Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 14}]] (* Mats Granvik, Jun 26 2014 *)

CROSSREFS

Cf. A018819 [From Gary W. Adamson, Nov 21 2009]

Cf. A129527, A016741 [From Gary W. Adamson, Nov 27 2009]

Sequence in context: A014024 A014039 A016410 * A115358 A117904 A071003

Adjacent sequences:  A115358 A115359 A115360 * A115362 A115363 A115364

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jan 21 2006

STATUS

approved

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Last modified October 25 15:08 EDT 2014. Contains 248556 sequences.