0,8

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

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.

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

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}

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

Largest element in each row gives A077419.

Sequence in context: A029339 A029364 A122586 this_sequence A069010 A087048 A109700

Adjacent sequences: A079484 A079485 A079486 this_sequence A079488 A079489 A079490

nonn,tabl

N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2003