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

0,8

Comments

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

Links

Table of n, a(n) for n=0..86.

Formula

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

Example

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.

Sequence in context: A077618 A356859 A085863 * A344478 A335489 A281188

Adjacent sequences: A220351 A220352 A220353 * A220355 A220356 A220357

Keyword

nonn,tabf

Author

Philippe Deléham, Apr 13 2013

Status

approved