The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261547 The 3 X 3 X ... X 3 dots problem (3, n times): minimal number of straight lines (connected at their endpoints) required to pass through 3^n dots arranged in a 3 X 3 X ... X 3 grid. 3
 1, 1, 4, 13, 40, 121, 364, 1093, 3280, 9841, 29524, 88573, 265720, 797161, 2391484, 7174453, 21523360, 64570081, 193710244, 581130733, 1743392200, 5230176601, 15690529804, 47071589413, 141214768240, 423644304721, 1270932914164 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Except for the first term a duplicate of A003462. This is an n-dimensional generalization of the well-known "Nine Dots Problem". Except for n < 2, the a(n) represent "outside the box" solutions, but (for any n) the minimal covering trail C(n) is still inside a box of hyper)-volume 3^n units^n. - Marco Ripà, Jul 19 2020 LINKS M. Ripà, Solving the 106 years old 3^k Points Problem with the Clockwise-algorithm, ResearchGate, 2020 (DOI: 10.13140/RG.2.2.34972.92802). M. Ripà, Solving the n_1 <= n_2 <= n_3 Points Problem for n_3 < 6, ResearchGate, 2020 (DOI: 10.13140/RG.2.2.12199.57769/1). M. Ripà, The rectangular spiral or the n1 X n2 X ... X nk Points Problem, Notes on Number Theory and Discrete Mathematics, 2014, 20(1), 59-71. Wikipedia, Nine dots puzzle FORMULA a(n) = (3^n - 1)/2 = A003462(n), for n >= 1. - Marco Ripà, Jul 19 2020 EXAMPLE For n=5, a(5) = 121. You cannot touch (the centers of) the 3^5 = 243 points using fewer than 121 straight lines, following the "Nine Dots Puzzle" basic rules. CROSSREFS Cf. A003462, A058992, A225227. Sequence in context: A025567 A003462 A076040 * A091141 A098183 A171556 Adjacent sequences:  A261544 A261545 A261546 * A261548 A261549 A261550 KEYWORD nonn AUTHOR Marco Ripà, Aug 24 2015 EXTENSIONS a(4) added by Marco Ripà, Aug 06 2018 a(3)-a(4) corrected and more terms added by Marco Ripà, Jul 19 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)