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%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
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