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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, 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, ...
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
KEYWORD
nonn,tabf
AUTHOR
Philippe Deléham, Apr 13 2013
STATUS
approved