A160379 Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160117 using cubes.

0, 1, 27, 35, 235, 261, 881, 937, 2241, 2339, 4591, 4743, 8207, 8425, 13365, 13661, 20341, 20727, 29411, 29899, 40851, 41453, 54937, 55665, 71945, 72811, 92151, 93167, 115831, 117009, 143261, 144613, 174717, 176255, 210475, 212211, 250811, 252757, 296001

Offset

0,3

Comments

Each cell has 26 neighbors.

Links

Table of n, a(n) for n=0..38.

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.]

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

a(2n) = 46n^3 - 57n^2 + 57n - 19 for n>=1, a(2n+1) = 46n^3 - 51n^2 + 57n - 17 for n>=1. [Nathaniel Johnston, Nov 06 2010]

G.f.: x*(18*x^3+x^2+26*x+1)*(x^4+4*x^2+1) / ((x-1)^4*(x+1)^3). - Colin Barker, Feb 28 2013

Crossrefs

Cf. A139250, A139251, A160117, A160118, A116119, A160160.

Sequence in context: A098883 A326893 A160119 * A351473 A152053 A166649

Adjacent sequences: A160376 A160377 A160378 * A160380 A160381 A160382

Keyword

nonn,easy

Author

Omar E. Pol, May 11 2009

Extensions

Edited by Omar E. Pol, Sep 05 2009

a(6) - a(27) from Nathaniel Johnston, Nov 06 2010

a(28) - a(38) from Colin Barker, Feb 28 2013

Status

approved