A160796 Total number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton which is the "corner" structure corresponding to A160118.

0, 1, 8, 11, 32, 35, 56, 65, 128, 131, 152, 161, 224, 233, 296, 323, 512, 515, 536, 545, 608, 617, 680, 707, 896, 905, 968, 995, 1184, 1211, 1400, 1481, 2048, 2051, 2072, 2081, 2144, 2153, 2216, 2243, 2432, 2441, 2504, 2531, 2720, 2747, 2936, 3017, 3584, 3593, 3656

Offset

0,3

Comments

This bears the same relationship to A160118 as A153006 does to A139250.

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = 2 + (3/4)*(A160118(n) - 1) if n >= 2.

Example

If we label the generations of cells turned ON by consecutive numbers we get the cell pattern shown below:
..9...............9
...888.888.888.888.
...878.878.878.878.
...8866688.8866688.
.....656.....656...
...8866444.4446688.
...878.434.434.878.
...888.4422244.888.
.........212.......
00000000002244.888.
0000000000.434.878.
0000000000.4446688.
0000000000...656...
0000000000.8866688.
0000000000.878.878.
0000000000.888.888.
0000000000........9
0000000000.........
0000000000.........

Mathematica

With[{d = 2}, wt[n_] := DigitCount[n, 2, 1]; a[n_] := (5 + 3 * If[OddQ[n], 3^d + (2^d)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, (n - 1)/2}] + (2^d)*(3^d - 2)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, (n - 3)/2}], 3^d + (2^d)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, n/2 - 1}] + (2^d)*(3^d - 2)*Sum[(2^d - 1)^(wt[k] - 1), {k, 1, n/2 - 1}]]) / 4; a[0] = 0; a[1] = 1; Array[a, 50, 0]] (* Amiram Eldar, Aug 01 2023 *)

Crossrefs

Cf. A139250, A153006, A160797, A160798, A160412, A160118, A160416.

Sequence in context: A029615 A051791 A243975 * A160416 A056873 A303883

Adjacent sequences: A160793 A160794 A160795 * A160797 A160798 A160799

Keyword

nonn

Author

Omar E. Pol, Jun 13 2009, Jun 14 2009

Extensions

Entry revised by Omar E. Pol and N. J. A. Sloane, Feb 16 2010

More terms from Nathaniel Johnston, Nov 13 2010

Corrected by Sean A. Irvine, Mar 23 2011, in response to correction to A160118

More terms from Amiram Eldar, Aug 01 2023

Status

approved