|
|
A147614
|
|
a(n) = number of grid points that are covered after n-th stage of A139250, assuming the toothpicks have length 2.
|
|
15
|
|
|
0, 3, 7, 13, 19, 27, 39, 53, 63, 71, 83, 99, 119, 147, 183, 217, 235, 243, 255, 271, 291, 319, 355, 391, 419, 447, 487, 539, 607, 699, 803, 885, 919, 927, 939, 955, 975, 1003, 1039, 1075, 1103, 1131, 1171, 1223, 1291, 1383, 1487, 1571, 1615
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
a(n) is also the number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the toothpick structure of A139250. [From Omar E. Pol, May 18 2009]
It appears that the number of grid points that are covered after n-th stage of A139250, assuming the toothpicks have length 2*k, is equal to (2*k-2) * A139250(n) + a(n), k>0. See formulas in A160420 and A160422. [From Omar E. Pol, Nov 15 2010]
More generally, it appears that a(n) is also the number of grid points that are covered by the "special points" of the toothpicks of A139250, after n-th stage, assuming the toothpicks have length 2*k, k>0 and that each toothpick has three special points: the midpoint and two endpoints.
Note that if k>1 then also there are 2*k-2 grid points that are covered by each toothpick, but these points are not considered for this sequence. [From Omar E. Pol, Nov 15 2010]
It appears that a(n)/A139250(n) converge to 4/3.
It appears that a(n)/A160124(n) converge to 2.
It appears that a(n)/A139252(n) converge to 4.
(End)
|
|
LINKS
|
|
|
FORMULA
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|