A156064 Inverse of Riordan array (1/(1-x^4), x/(1-x^4)), A156062.
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, 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, 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
Offset: 0
Examples
Triangle begins
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, 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, 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;
Production matrix is
0, 1;
0, 0, 1;
0, 0, 0, 1;
-1, 0, 0, 0, 1;
0, -1, 0, 0, 0, 1;
0, 0, -1, 0, 0, 0, 1;
0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1;
Links
- Chai Wah Wu, Record values in appending and prepending bitstrings to runs of binary digits, arXiv:1810.02293 [math.NT], 2018.
Comments