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%I #19 Aug 01 2023 06:56:02
%S 0,1,8,11,32,35,56,65,128,131,152,161,224,233,296,323,512,515,536,545,
%T 608,617,680,707,896,905,968,995,1184,1211,1400,1481,2048,2051,2072,
%U 2081,2144,2153,2216,2243,2432,2441,2504,2531,2720,2747,2936,3017,3584,3593,3656
%N Total number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton which is the "corner" structure corresponding to A160118.
%C This bears the same relationship to A160118 as A153006 does to A139250.
%F a(n) = 2 + (3/4)*(A160118(n) - 1) if n >= 2.
%e If we label the generations of cells turned ON by consecutive numbers we get the cell pattern shown below:
%e ..9...............9
%e ...888.888.888.888.
%e ...878.878.878.878.
%e ...8866688.8866688.
%e .....656.....656...
%e ...8866444.4446688.
%e ...878.434.434.878.
%e ...888.4422244.888.
%e .........212.......
%e 00000000002244.888.
%e 0000000000.434.878.
%e 0000000000.4446688.
%e 0000000000...656...
%e 0000000000.8866688.
%e 0000000000.878.878.
%e 0000000000.888.888.
%e 0000000000........9
%e 0000000000.........
%e 0000000000.........
%t 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 *)
%Y Cf. A139250, A153006, A160797, A160798, A160412, A160118, A160416.
%K nonn
%O 0,3
%A _Omar E. Pol_, Jun 13 2009, Jun 14 2009
%E Entry revised by _Omar E. Pol_ and _N. J. A. Sloane_, Feb 16 2010
%E More terms from _Nathaniel Johnston_, Nov 13 2010
%E Corrected by _Sean A. Irvine_, Mar 23 2011, in response to correction to A160118
%E More terms from _Amiram Eldar_, Aug 01 2023
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