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A114729 One of a family of six fractal sequences that transform to each other. 7
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

Table of n, a(n) for n=1..104.

EXAMPLE

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

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]];

a[6] (* Birkas Gyorgy, Apr 21 2011 *)

CROSSREFS

Cf. A114730, A114731, A114732, A114733, A114733.

Sequence in context: A274884 A076224 A286582 * A186037 A144365 A152197

Adjacent sequences:  A114726 A114727 A114728 * A114730 A114731 A114732

KEYWORD

nonn

AUTHOR

Kerry Mitchell, Dec 28 2005

STATUS

approved

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Last modified September 27 03:05 EDT 2021. Contains 347673 sequences. (Running on oeis4.)