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

Author

Paul Barry, Oct 20 2009

Keywords

• easy
• sign
• tabl

Comments

Reverse and aerate A069270. First column is signed aerated version of A002293. Diagonal sums are A156065.

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.