A114729 - OEIS

%I #9 Nov 30 2016 23:46:14

%S 1,1,1,2,3,2,2,1,1,1,2,3,4,4,3,3,2,2,1,1,1,2,3,4,5,6,5,5,4,4,3,3,2,2,

%T 1,1,1,2,3,4,5,6,7,7,6,6,5,5,4,4,3,3,2,2,1,1,1,2,3,4,5,6,7,8,9,8,8,7,

%U 7,6,6,5,5,4,4,3,3,2,2,1,1,1,2,3,4,5,6,7,8,9,10,10,9,9,8,8,7,7,6,6,5,5,4,4

%N One of a family of six fractal sequences that transform to each other.

%C 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:

%C - A upper trims to B

%C - B upper trims to C

%C - C upper trims to A

%C - A lower trims to C

%C - B lower trims to A

%C - C lower trims to B

%C - D gives the number of times each element of A occurs

%C - E gives the number of times each element of B occurs

%C - F gives the number of times each element of C occurs

%C - A gives the number of times each element of D occurs

%C - B gives the number of times each element of E occurs

%C - C gives the number of times each element of F occurs

%C - D lower trims to E

%C - E lower trims to F

%C - F lower trims to D

%C - D upper trims to F

%C - E upper trims to D

%C - F upper trims to E

%e D(7)=3 and that's the second 3 in sequence D, so A(7)=2.

%t c[n_] := Flatten[ Table[{Range[3 Floor[(k - 1)/2] + 2],

%t      Table[{i, i}, {i, Floor[k/2] + k, 1, -1}]}, {k, n}]];

%t uppertrim[list_] := Fold[DeleteCases[#1, #2, 1, 1] &, list, Range[Max[list]]];

%t lowertrim[list_] := DeleteCases[list - 1, 0];

%t numbertimes[list_] := Table[Length@Position[Take[list, k], list[[k]]], {k, Length[list]}];

%t a[n_] := uppertrim[c[n]];

%t b[n_] := uppertrim[a[n]];

%t d[n_] := numbertimes[a[n]];

%t e[n_] := numbertimes[b[n]];

%t f[n_] := numbertimes[c[n]];

%t a[6] (* _Birkas Gyorgy_, Apr 21 2011 *)

%Y Cf. A114730, A114731, A114732, A114733, A114733.

%K nonn

%O 1,4

%A _Kerry Mitchell_, Dec 28 2005