This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A115361 Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation). 23

%I

%S 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,

%T 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,

%U 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

%N Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation).

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

%C Eigensequence of triangle A115361 = A018819 starting with offset 1: (1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20,...). [From _Gary W. Adamson_, Nov 21 2009]

%C Contribution from _Gary W. Adamson_, Nov 27 2009: (Start)

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

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

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

%e Triangle begins

%e 1;

%e 1,1;

%e 0,0,1;

%e 1,1,0,1;

%e 0,0,0,0,1;

%e 0,0,1,0,0,1;

%e 0,0,0,0,0,0,1;

%e 1,1,0,1,0,0,0,1;

%e 0,0,0,0,0,0,0,0,1;

%e 0,0,0,0,1,0,0,0,0,1;

%e 0,0,0,0,0,0,0,0,0,0,1;

%p A115361 := proc(n,k)

%p for j from 0 do

%p if k+(2*j-1)*(k+1) > n then

%p return 0 ;

%p elif k+(2^j-1)*(k+1) = n then

%p return 1 ;

%p end if;

%p end do;

%p end proc: # _R. J. Mathar_, Jul 14 2012

%Y Cf. A018819 [From _Gary W. Adamson_, Nov 21 2009]

%Y Cf. A129527, A016741 [From _Gary W. Adamson_, Nov 27 2009]

%K easy,nonn,tabl

%O 0,1

%A _Paul Barry_, Jan 21 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .