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A079487
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Triangle read by rows giving Whitney numbers T(n,k) of Fibonacci lattices.
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2
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 3, 3, 3, 2, 1, 1, 3, 4, 5, 4, 3, 1, 1, 4, 6, 7, 7, 5, 3, 1, 1, 4, 7, 10, 11, 10, 7, 4, 1, 1, 5, 10, 14, 17, 16, 13, 8, 4, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Row sums are Fibonacii numbers A000045. - Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 07 2006
This is the second kind of Whitney numbers, which count elements, not to be confused with the first kind, which sum Mobius functions. - Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), May 07 2008
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REFERENCES
| E. Munarini and N. Zagaglia Salvi, On the Rank Polynomial of the Lattice of Order Ideals of Fences and Crowns, Discrete Mathematics 259 (2002), 163-177.
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FORMULA
| Define polynomials by: if k is odd then p(k, x) = x*p(k - 1, x) + p(k - 2, x); if k is even then: p(k, x) = p(k - 1, x) + x^2*p(k - 2, x). Triangle gives array of coefficients. - Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 07 2006
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EXAMPLE
| Triangle begins:
{1},
{1, 1},
{1, 1, 1},
{1, 2, 1, 1},
{1, 2, 2, 2, 1},
{1, 3, 3, 3, 2, 1},
{1, 3, 4, 5, 4, 3, 1},
{1, 4, 6, 7, 7, 5, 3, 1},
{1, 4, 7, 10, 11, 10, 7, 4, 1},
{1, 5, 10, 14, 17, 16, 13, 8, 4, 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] == 1, 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] - Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 07 2006
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CROSSREFS
| Largest element in each row gives A077419.
Sequence in context: A029339 A029364 A122586 * A069010 A087048 A109700
Adjacent sequences: A079484 A079485 A079486 * A079488 A079489 A079490
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2003
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