Original entry on oeis.org
1, 26, 56, 260, 56, 392, 392, 2192, 56, 392, 392, 2744, 392, 2744, 2744, 16952, 56, 392, 392, 2744, 392, 2744, 2744, 19208, 392, 2744, 2744, 19208, 2744, 19208, 19208, 125336, 56, 392, 392, 2744, 392, 2744, 2744, 19208, 392, 2744, 2744, 19208, 2744, 19208, 19208
Offset: 1
From _Omar E. Pol_, Mar 15 2020: (Start)
Written as an irregular triangle in which row lengths give A011782 the sequence begins:
1;
26;
56, 260;
56, 392, 392, 2192;
56, 392, 392, 2744, 392, 2744, 2744, 16952;
56, 392, 392, 2744, 392, 2744, 2744, 19208, 392, 2744, 2744, 19208, 2744, ...
(End)
-
f(n) = 8*7^hammingweight(n-1); \\ A160429
ispow2(n) = my(k); (n==2) || (ispower(n,,&k) && (k==2));
a(n) = if (n==1, 1, if (ispow2(n), f(n) - 3*n*(3*n - 1), f(n))); \\ Michel Marcus, Mar 15 2020
A160428
Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160410, using cubes.
Original entry on oeis.org
0, 8, 64, 120, 512, 568, 960, 1352, 4096, 4152, 4544, 4936, 7680, 8072, 10816, 13560, 32768, 32824, 33216, 33608, 36352, 36744, 39488, 42232, 61440, 61832, 64576, 67320, 86528, 89272, 108480, 127688, 262144, 262200, 262592, 262984, 265728, 266120, 268864, 271608
Offset: 0
- Michael De Vlieger, Table of n, a(n) for n = 0..1000
- 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.]
- Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 33.
- N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
- Index entries for sequences related to cellular automata
-
a[n_] := 8*Sum[7^DigitCount[k, 2, 1], {k, 0, n - 1}]; Array[a, 40, 0] (* Michael De Vlieger, Nov 01 2022 *)
Original entry on oeis.org
1, 26, 8, 200, 26, 620, 56, 1304, 98, 2252, 152, 3464, 218, 4940, 296, 6680, 386, 8684, 488, 10952, 602, 13484, 728, 16280, 866, 19340, 1016, 22664, 1178, 26252, 1352, 30104, 1538, 34220, 1736, 38600, 1946, 43244, 2168, 48152, 2402, 53324, 2648, 58760, 2906
Offset: 1
-
LinearRecurrence[{0,3,0,-3,0,1},{1,26,8,200,26,620,56,1304},50] (* Harvey P. Dale, May 19 2025 *)
-
Vec(-x*(18*x^3+x^2+26*x+1)*(x^4+4*x^2+1)/((x-1)^3*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 17 2013
Original entry on oeis.org
1, 26, 8, 200, 8, 200, 56, 1400, 8, 200, 56, 1400, 56, 1400, 392, 9800, 8, 200, 56, 1400, 56, 1400, 392, 9800, 56, 1400, 392, 9800, 392, 9800, 2744, 68600
Offset: 1
Showing 1-4 of 4 results.