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 A114732 One of a family of six fractal sequences that transforms into each other. 6
 1, 2, 3, 1, 1, 2, 3, 4, 5, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 10, 8, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 13, 11, 9, 7, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 2, 3, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let A be the sequence A114729 (1, 1, 1, 2, 3, 2, 2, 1, 1, 1, ...), B be the sequence A114730 (1, 1, 2, 2, 1, 1, 1, 2, 3, 4, ...) and C be the sequence A114731 (1, 2, 1, 1, 1, 2, 3, 3, 2, 2, ...). Let D be the sequence A114732 (1, 2, 3, 1, 1, 2, 3, 4, 5, 6, ...), E be the sequence A114733 (1, 2, 1, 2, 3, 4, 5, 3, 1, 1, ...) and F be the sequence A114734 (1, 1, 2, 3, 4, 2, 1, 2, 3, 4, ...). Then: - A upper trims to B - B upper trims to C - C upper trims to A - A lower trims to C - B lower trims to A - C lower trims to B - D gives the number of times each element of A occurs - E gives the number of times each element of B occurs - F gives the number of times each element of C occurs - A gives the number of times each element of D occurs - B gives the number of times each element of E occurs - C gives the number of times each element of F occurs - D lower trims to E - E lower trims to F - F lower trims to D - D upper trims to F - E upper trims to D - F upper trims to E LINKS FORMULA c[n_] := Flatten[ Table[{Range[3 Floor[(k - 1)/2] + 2],      Table[{i, i}, {i, Floor[k/2] + k, 1, -1}]}, {k, n}]]; uppertrim[list_] := Fold[DeleteCases[#1, #2, 1, 1] &, list, Range[Max[list]]]; lowertrim[list_] := DeleteCases[list - 1, 0]; numbertimes[list_] := Table[Length@Position[Take[list, k], list[[k]]], {k, Length[list]}]; a[n_] := uppertrim[c[n]]; b[n_] := uppertrim[a[n]]; d[n_] := numbertimes[a[n]]; e[n_] := numbertimes[b[n]]; f[n_] := numbertimes[c[n]]; d[6] (* Gyorgy Birkas, Apr 21, 2011 *) EXAMPLE A(5)=3 and that's the first 3 in that sequence, so D(5)=1. CROSSREFS Cf. A114729, A114730, A114731, A114733, A114734. Sequence in context: A157813 A111879 A193280 * A123338 A152735 A046226 Adjacent sequences:  A114729 A114730 A114731 * A114733 A114734 A114735 KEYWORD nonn AUTHOR Kerry Mitchell, Dec 28 2005 STATUS approved

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