STATUS
proposed
approved
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Revision History for A082870
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
STATUS
editing
proposed
COMMENTS
1, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 0, 0, 0, 0, ...
1, 2, 3, 2, 1, 0, 0, ...
1, 3, 6, 7, 6, 3, 1, ...
STATUS
proposed
editing
STATUS
editing
proposed
COMMENTS
From Gary W. Adamson, Nov 15 2016; : (Start)
... (where the k-th row is (1 + x + x^2)^k), let q(x) = (r(x) * r(x^3) * r(x^9) * r(x^27) * ...). Then q(x) is the binomial sequence beginning (1, k, ...). Example: (1, 3, 6, 10, ...) = q(x) with r(x) = (1, 3, 6, 7, 3, 1, 0, 0, 0). (End)
FORMULA
G.f.: x/(1 - x - x^2*y - x^3*y^2). - Vladeta Jovovic, May 30 2003
EXAMPLE
1,
1,
1, 1,
1, 2, 1,
1, 3, 3,
1, 4, 6, 2,
1, 5, 10, 7, 1,
1, 6, 15, 16, 6,
STATUS
proposed
editing
STATUS
editing
proposed
COMMENTS
From Gary W. Adamson, Nov 15 2016; (Start): With an alternative format:
With an alternative format:
... (where the k-th row is (1 + x + x^2)^k), let q(x) = (r(x) * r(x^3) * r(x^9) * r(x^27) * ...). Then q(x) is the binomial sequence beginning (1, k...). Example: (1, 3, 6, 10,...) = q(x) with r(x) = (1, 3, 6, 7, 3, 1, 0, 0, 0). (End)
STATUS
proposed
editing
STATUS
editing
proposed
COMMENTS
From Gary W. Adamson, Nov 15 2016; (Start): With an alternative format:
1, 0, 0, 0, 0, 0, 0,...
1, 1, 1, 0, 0, 0, 0,...
1, 2, 3, 2, 1, 0, 0,...
1, 3, 6, 7, 6, 3, 1,...
...(where the k-th row is (1 + x + x^2)^k), let q(x) = (r(x) * r(x^3) * r(x^9) * r(x^27) * ...). Then q(x) is the binomial sequence beginning (1, k...). Example: (1, 3, 6, 10,...) = q(x) with r(x) = (1, 3, 6, 7, 3, 1, 0, 0, 0). (End)
STATUS
approved
editing
STATUS
editing
approved