Search: id:A079487
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%I A079487
%S A079487 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,
%T A079487 5,3,1,1,4,7,10,11,10,7,4,1,1,5,10,14,17,16,13,8,4,1
%N A079487 Triangle read by rows giving Whitney numbers T(n,k) of Fibonacci lattices.
%C A079487 Row sums are Fibonacii numbers A000045. - Roger Bagula (rlbagulatftn(AT)yahoo.com), 
               Oct 07 2006
%C A079487 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
%D A079487 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.
%F A079487 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
%e A079487 Triangle begins:
%e A079487 {1},
%e A079487 {1, 1},
%e A079487 {1, 1, 1},
%e A079487 {1, 2, 1, 1},
%e A079487 {1, 2, 2, 2, 1},
%e A079487 {1, 3, 3, 3, 2, 1},
%e A079487 {1, 3, 4, 5, 4, 3, 1},
%e A079487 {1, 4, 6, 7, 7, 5, 3, 1},
%e A079487 {1, 4, 7, 10, 11, 10, 7, 4, 1},
%e A079487 {1, 5, 10, 14, 17, 16, 13, 8, 4, 1},
%e A079487 {1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1}
%t A079487 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
%Y A079487 Largest element in each row gives A077419.
%Y A079487 Sequence in context: A029339 A029364 A122586 this_sequence A069010 A087048 
               A109700
%Y A079487 Adjacent sequences: A079484 A079485 A079486 this_sequence A079488 A079489 
               A079490
%K A079487 nonn,tabl
%O A079487 0,8
%A A079487 N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2003

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