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A253281 Triangular array read by rows: T(h,k) = number of steps from (h,k) to (0,0), where allowable steps are as follows:  (x,y) -> (x-r, y) if r > 0, and (x,y) -> (y, r/3) otherwise, where r = x mod 3. 2
0, 1, 2, 1, 3, 2, 3, 3, 3, 4, 4, 4, 3, 5, 5, 4, 5, 4, 5, 6, 5, 3, 5, 5, 5, 6, 6, 4, 4, 4, 5, 6, 6, 6, 5, 5, 4, 5, 4, 6, 7, 6, 5, 6, 5, 5, 5, 5, 5, 7, 7, 5, 6, 6, 6, 6, 6, 5, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 8, 7, 6, 7, 7, 6, 7, 7, 5, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n >= 3, the number of pairs (h,k) satisfying T(h,k) = n is A078008(n+1) for n >= 0.  The number of pairs of the form (h,0) satisfying T(h,0) = n is A253718(n).

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

EXAMPLE

First ten rows:

0

1  2

1  3  2

3  3  3  4

4  4  3  5  5

4  5  4  5  6  5

3  5  5  5  6  6  4

4  4  5  6  6  6  5  5

4  5  4  6  7  6  5  6  5

5  5  5  5  7  7  5  6  6  6

Row 3 counts the pairs (2,0), (1,1), (0,2), for which the paths are as shown here:

(2,0) -> (0,0) (1 step)

(1,1) -> (0,1) -> (1,0) -> (0,0) (3 steps)

(0,2) -> (2,0) -> (0,0) (2 steps)

MATHEMATICA

f[{x_, y_}] := If[IntegerQ[x/3], {y, x/3}, {x - Mod[x, 3], y}];

g[{x_, y_}] := Drop[FixedPointList[f, {x, y}], -1];

h[{x_, y_}] := -1 + Length[g[{x, y}]];

t = Table[h[{n - k, k}], {n, 0, 20}, {k, 0, n}];

TableForm[t] (* A253281 array *)

Flatten[t]   (* A253281 sequence *)

CROSSREFS

Cf. A078008, A257569, A253718.

Sequence in context: A087825 A263100 A261388 * A029206 A029200 A317243

Adjacent sequences:  A253278 A253279 A253280 * A253282 A253283 A253284

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, May 02 2015

STATUS

approved

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Last modified October 27 07:47 EDT 2021. Contains 348272 sequences. (Running on oeis4.)