A127969 -id:A127969 - cp's OEIS frontend

A127972 Number triangle A127969 modulo 2.

1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0

Offset: 0

Paul Barry, Feb 09 2007

Row sums are A127973.

			Triangle begins
1,
1, 1,
1, 0, 1,
1, 0, 0, 1,
0, 0, 1, 0, 1,
1, 0, 1, 0, 1, 1,
0, 0, 1, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 1, 0, 0, 0, 1,
1, 0, 1, 0, 0, 0, 0, 0, 1, 1,
0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1,
1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1

A127967 A right-skewed Pascal triangle, with interspersed 1's on main diagonal.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 0, 4, 0, 3, 1, 1, 0, 5, 0, 6, 0, 1, 1, 0, 6, 0, 10, 0, 4, 1, 1, 0, 7, 0, 15, 0, 10, 0, 1, 1, 0, 8, 0, 21, 0, 20, 0, 5, 1, 1, 0, 9, 0, 28, 0, 35, 0, 15, 0, 1, 1, 0, 10, 0, 36, 0, 56, 0, 35, 0, 6, 1

Offset: 0

Paul Barry, Feb 09 2007

Linked to Fibonacci numbers by row sums A127968. Inverse A127969 is linked to Genocchi numbers by its first column.

			Triangle begins
  1;
  1, 1;
  1, 0,  1;
  1, 0,  2, 1;
  1, 0,  3, 0,  1;
  1, 0,  4, 0,  3, 1;
  1, 0,  5, 0,  6, 0,  1;
  1, 0,  6, 0, 10, 0,  4, 1;
  1, 0,  7, 0, 15, 0, 10, 0,  1;
  1, 0,  8, 0, 21, 0, 20, 0,  5, 1;
  1, 0,  9, 0, 28, 0, 35, 0, 15, 0,  1;
  1, 0, 10, 0, 36, 0, 56, 0, 35, 0,  6, 1;
  1, 0, 11, 0, 45, 0, 84, 0, 70, 0, 21, 0, 1;

Cf. A127968, A127969.

Column k is generated by x^(-2)*(x*(1-x)^(-1/2))^(k+2), where non-integer values are set to 0; or, column k has g.f. x^k/(1-x)^(1+k/2) if k is even, x^k if k is odd.

cp's OEIS Frontend

A127972 Number triangle A127969 modulo 2.

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