Search: id:A115361
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%I A115361
%S A115361 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,
%T A115361 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,
%U A115361 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 A115361 Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation).
%C A115361 Row sums are the 'ruler function' A001511. Columns are stretched Fredholm-Rueppel 
               sequences. Inverse is A115359.
%C A115361 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 
               (qntmpkt(AT)yahoo.com), Nov 21 2009]
%C A115361 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 27 2009: 
               (Start)
%C A115361 A115361 * [1, 2, 3,...] = A129527 = (1, 3, 3, 7, 5, 9, 7, 15,...).
%C A115361 (A115361)^(-1) * [1, 2, 3,...] = A115359 * [1, 2, 3,...] = A026741 starting 
               /Q (1, 1, 3, 2, 5, 3, 7, 4, 9,...). (End)
%F A115361 Number triangle whose k-th column has g.f. x^k*sum{j>=0, (x^(2j-1))^(k+1)}.
%e A115361 Triangle begins
%e A115361 1;
%e A115361 1,1;
%e A115361 0,0,1;
%e A115361 1,1,0,1;
%e A115361 0,0,0,0,1;
%e A115361 0,0,1,0,0,1;
%e A115361 0,0,0,0,0,0,1;
%e A115361 1,1,0,1,0,0,0,1;
%e A115361 0,0,0,0,0,0,0,0,1;
%e A115361 0,0,0,0,1,0,0,0,0,1;
%e A115361 0,0,0,0,0,0,0,0,0,0,1;
%Y A115361 Sequence in context: A014024 A014039 A016410 this_sequence A115358 A117904 
               A115944
%Y A115361 Cf. A018819 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 21 2009]
%Y A115361 Adjacent sequences: A115358 A115359 A115360 this_sequence A115362 A115363 
               A115364
%Y A115361 Cf. A129527, A016741 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 
               27 2009]
%K A115361 easy,nonn,tabl,new
%O A115361 0,1
%A A115361 Paul Barry (pbarry(AT)wit.ie), Jan 21 2006

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