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 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 (list; graph; refs; listen; history; text; internal format)
 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 n-1). A toothpick added at stage n may touch other toothpicks added at stage n. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..8194 Rémy Sigrist, Illustration of the structure at stage 16 Rémy Sigrist, PARI program Index entries for sequences related to cellular automata Index entries for sequences related to toothpick sequences 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 Cf. A139250, A351838. Sequence in context: A211434 A182388 A080335 * A089109 A100449 A146284 Adjacent sequences: A351834 A351835 A351836 * A351838 A351839 A351840 KEYWORD nonn AUTHOR Rémy Sigrist, Feb 21 2022 STATUS approved

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Last modified February 26 15:44 EST 2024. Contains 370352 sequences. (Running on oeis4.)