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 A160160 Toothpick sequence in the three-dimensional grid. 23
 0, 1, 3, 7, 15, 23, 31, 39, 55, 87, 143, 175, 191, 199, 215, 247, 303, 359, 423, 503, 655, 887, 1239, 1383, 1431, 1463, 1487, 1527, 1583, 1639, 1703, 1783, 1935, 2167, 2519, 2735, 2903, 3079, 3351, 3711, 4207, 4655, 5191, 5855, 7023, 8511, 10511, 11279, 11583, 11919, 12183, 12375, 12487, 12607 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Similar to A139250, except the toothpicks are placed in three dimensions, not two. The first toothpick is in the z direction. Thereafter, new toothpicks are placed at free ends, as in A139250, perpendicular to the existing toothpick, but choosing in rotation the x-direction, y-direction, z-direction, x-direction, etc. The graph of this sequence has a nice self-similar shape: it looks the when the x-range is multiplied by 2, e.g. a(0..125) vs a(0..250) or a(0..500). - M. F. Hasler, Dec 12 2018 LINKS M. F. Hasler, Table of n, a(n) for n = 0..500 David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.] R. J. Mathar, C++ program R. J. Mathar, View after stage 1 R. J. Mathar, View after stage 2 R. J. Mathar, View after stage 3 R. J. Mathar, View after stage 4 R. J. Mathar, View after stage 5 R. J. Mathar, View after stage 6 R. J. Mathar, View after stage 7 R. J. Mathar, View after stage 8 R. J. Mathar, View after stage 9 R. J. Mathar, View after stage 10 N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS Alex van den Brandhof and Paul Levrie, Tandenstokerrij, Pythagoras, Viskundetijdschrift voor Jongeren, 55ste Jaargang, Nummer 6, Juni 2016, (see page 19 and the back cover). FORMULA Partial sums of A160161: a(n) = Sum_{1 <= k <= n} A160161(k) for all n >= 0. - M. F. Hasler, Dec 12 2018 PROG (PARI) A160160_vec(n, o=1)={local(s(U)=[Vecsmall(Vec(V)+U)|V<-E], E=[Vecsmall([1, 1, 1])], J=[], M, A, B, U); [if(i>4, M+=8*#E=setminus(setunion(A=s(U=matid(3)[i%3+1, ]), B=select(vecmin, s(-U))), J=setunion(setunion(setintersect(A, B), E), J)), M=1<

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Last modified November 29 16:39 EST 2022. Contains 358431 sequences. (Running on oeis4.)