|
| |
|
|
A114734
|
|
One of a family of six fractal sequences that transform into each other.
|
|
6
| |
|
|
1, 1, 2, 3, 4, 2, 1, 2, 3, 4, 5, 6, 7, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 8, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 11, 9, 7, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 14, 12, 10, 8, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 17
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
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
|
|
|
EXAMPLE
| C(10)=2 and it is the fourth 2 in the sequence, so F(10)=4.
|
|
|
MATHEMATICA
| 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]];
f[6] (* Gyorgy Birkas, Apr 21, 2011 *)
|
|
|
CROSSREFS
| Cf. A114729, A114730, A114731, A114732, A114733.
Sequence in context: A037838 A165052 A107474 * A182710 A182711 A138136
Adjacent sequences: A114731 A114732 A114733 * A114735 A114736 A114737
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Kerry Mitchell (lkmitch(AT)gmail.com), Dec 28 2005
|
| |
|
|
