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A123245
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A Switched recursive polynomial that related to A079487 by reversing coefficient order: even: p(k, x) = x*p(k - 1, x) + p(k - 2, x); odd: p(k, x) =p(k - 1, x) + x^2*p(k - 2, x).
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0
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 3, 1, 1, 3, 4, 5, 4, 3, 1, 1, 3, 5, 7, 7, 6, 4, 1, 1, 4, 7, 10, 11, 10, 7, 4, 1, 1, 4, 8, 13, 16, 17, 14, 10, 5, 1, 1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| Row sums give Fibonacii A000045: {1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597}
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FORMULA
| even: p(k, x) = x*p(k - 1, x) + p(k - 2, x); odd: p(k, x) =p(k - 1, x) + x^2*p(k - 2, x)
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EXAMPLE
| {1},
{1, 1},
{1, 1, 1},
{1, 1, 2, 1},
{1, 2, 2, 2, 1},
{1, 2, 3, 3, 3, 1},
{1, 3, 4, 5, 4, 3, 1},
{1, 3, 5, 7, 7, 6, 4, 1},
{1, 4, 7, 10, 11, 10, 7, 4, 1},
{1, 4, 8, 13, 16, 17, 14, 10, 5, 1},
{1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1}
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MATHEMATICA
| p[0, x] = 1; p[1, x] = x + 1; p[k_, x_] := p[k, x] = If[ Mod[k, 2] == 0, x*p[k - 1, x] + p[k - 2, x], p[k - 1, x] + x^2*p[k - 2, x]]; Table[Expand[p[n, x]], {n, 0, 10}] Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, Length[CoefficientList[p[n, x], x]]}], {n, 0, 15}] w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
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CROSSREFS
| Cf. A000045, A079487.
Sequence in context: A096492 A053874 A170906 * A110535 A033941 A053256
Adjacent sequences: A123242 A123243 A123244 * A123246 A123247 A123248
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 07 2006
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