A220354 Irregular triangle T(n,k), read by rows; row n gives coefficients in expansion of P_n(x), which is defined by: P_0(x) = 1, P_n(x) = P_(n-1)(x)+x if n odd, P_n(x) = P_(n-1)(x)*x if n even.

1, 1, 1, 0, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1, 0, 0, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 0

Author

Philippe Deléham, Apr 13 2013

Keywords

• nonn
• tabf

Comments

Row lengths are: 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, ...

Examples

			Irregular triangle begins:
1
1, 1
0, 1, 1
0, 2, 1
0, 0, 2, 1
0, 1, 2, 1
0, 0, 1, 2, 1
0, 1, 1, 2, 1
0, 0, 1, 1, 2, 1
0, 1, 1, 1, 2, 1
0, 0, 1, 1, 1, 2, 1
0, 1, 1, 1, 1, 2, 1
0, 0, 1, 1, 1, 1, 2, 1
0, 1, 1, 1, 1, 1, 2, 1
...
		

Crossrefs

Cf. A219605.

Formula

Sum_(T(n,k)*x^k, k>=0) = A019590(n+1), A008619(n+1), A123208(n) for x = 0, 1, 2 respectively.