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%I #7 Dec 25 2018 22:23:17
%S 1,0,1,0,0,1,0,0,0,1,-1,0,0,0,1,0,-2,0,0,0,1,0,0,-3,0,0,0,1,0,0,0,-4,
%T 0,0,0,1,4,0,0,0,-5,0,0,0,1,0,9,0,0,0,-6,0,0,0,1,0,0,15,0,0,0,-7,0,0,
%U 0,1,0,0,0,22,0,0,0,-8,0,0,0,1,-22,0,0,0,30,0,0,0,-9,0,0,0,1,0,-52,0,0,0,39
%N Inverse of Riordan array (1/(1-x^4), x/(1-x^4)), A156062.
%C Reverse and aerate A069270. First column is signed aerated version of A002293. Diagonal sums are A156065.
%H Chai Wah Wu, <a href="https://arxiv.org/abs/1810.02293">Record values in appending and prepending bitstrings to runs of binary digits</a>, arXiv:1810.02293 [math.NT], 2018.
%e Triangle begins
%e 1;
%e 0, 1;
%e 0, 0, 1;
%e 0, 0, 0, 1;
%e -1, 0, 0, 0, 1;
%e 0, -2, 0, 0, 0, 1;
%e 0, 0, -3, 0, 0, 0, 1;
%e 0, 0, 0, -4, 0, 0, 0, 1;
%e 4, 0, 0, 0, -5, 0, 0, 0, 1;
%e 0, 9, 0, 0, 0, -6, 0, 0, 0, 1;
%e 0, 0, 15, 0, 0, 0, -7, 0, 0, 0, 1;
%e 0, 0, 0, 22, 0, 0, 0, -8, 0, 0, 0, 1;
%e -22, 0, 0, 0, 30, 0, 0, 0, -9, 0, 0, 0, 1;
%e Production matrix is
%e 0, 1;
%e 0, 0, 1;
%e 0, 0, 0, 1;
%e -1, 0, 0, 0, 1;
%e 0, -1, 0, 0, 0, 1;
%e 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
%K easy,sign,tabl
%O 0,17
%A _Paul Barry_, Oct 20 2009
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