

A351837


Consider a variant of the toothpick sequence (A139250) where each new toothpick, except the first, touches exactly one existing toothpick at the ends, this one being in the prior stage; a(n) is the total number of toothpicks at stage n.


2



0, 1, 5, 9, 17, 25, 37, 53, 69, 77, 89, 109, 133, 161, 201, 249, 281, 289, 301, 321, 345, 373, 413, 465, 505, 533, 577, 641, 717, 813, 941, 1069, 1133, 1141, 1153, 1173, 1197, 1225, 1265, 1317, 1357, 1385, 1429, 1493, 1569, 1665, 1793, 1925, 1997, 2025, 2069
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OFFSET

0,3


COMMENTS

We consider toothpicks of length 1, parallel to the X and Y axes.
We start at stage 0 with no toothpicks.
At stage 1 we place one toothpick anywhere in the plane.
At stage n > 1, we consider all exposed ends E (i.e. in contact with no other toothpick) and attach perpendicular toothpicks in contact with E by one end provided that they won't touch other existing toothpicks (from stages 1 to n1).
A toothpick added at stage n may touch other toothpicks added at stage n.


LINKS



EXAMPLE

The configuration at stage 4 can be depicted as follows (stars representing ends and toothpicks being labeled with their stage of appearance):
.
* *
 
4 4
 
*3* *3*
   
4 2 2 4
   
* *1* *
   
4 2 2 4
   
*3* *3*
 
4 4
 
* *
.
 so a(4) = 1 + 4 + 4 + 8 = 17.


PROG

(PARI) See Links section.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



