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 A172453 A combinatorial triangle based on A004001 product sequences:c(n)=If[n == 1, 1, Product[A004001[m], {m, 1, n}]];t(n,m)=c(n)/(c(m)*c(n-m)) 0
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 6, 3, 1, 1, 4, 12, 12, 12, 4, 1, 1, 4, 16, 24, 24, 16, 4, 1, 1, 4, 16, 32, 48, 32, 16, 4, 1, 1, 5, 20, 40, 80, 80, 40, 20, 5, 1, 1, 6, 30, 60, 120, 160, 120, 60, 30, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are: {1, 2, 3, 6, 10, 20, 46, 90, 154, 292, 594,...}. The Modulo two pattern appears to be symmetrically chaotic: ListDensityPlot[Table[Table[If[n >= m, Mod[t[ n, m], 2], 0], {m, 0, 32}], {n, 0, 32}], Mesh -> False, Axes -> False] LINKS FORMULA c(n)=If[n == 1, 1, Product[A004001[m], {m, 1, n}]] t(n,m)=c(n)/(c(m)*c(n-m)) EXAMPLE {1}, {1, 1}, {1, 1, 1}, {1, 2, 2, 1}, {1, 2, 4, 2, 1}, {1, 3, 6, 6, 3, 1}, {1, 4, 12, 12, 12, 4, 1}, {1, 4, 16, 24, 24, 16, 4, 1}, {1, 4, 16, 32, 48, 32, 16, 4, 1}, {1, 5, 20, 40, 80, 80, 40, 20, 5, 1}, {1, 6, 30, 60, 120, 160, 120, 60, 30, 6, 1}} MATHEMATICA (*A004001*) f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 1]] + f[n - f[n - 1]]; c[n_] := If[n == 1, 1, Product[f[m], {m, 1, n}]]; t[n_, m_] := c[n]/(c[m]*c[n - m]); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A220777 A088855 A034851 * A172479 A122085 A209612 Adjacent sequences:  A172450 A172451 A172452 * A172454 A172455 A172456 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 03 2010 STATUS approved

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Last modified December 9 17:22 EST 2018. Contains 318023 sequences. (Running on oeis4.)