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%I #24 Feb 03 2024 10:16:39
%S 1,8,4,28,4,28,12,84,4,28,12,84,12,84,36,252,4,28,12,84,12,84,36,252,
%T 12,84,36,252,36,252,108,756,4,28,12,84,12,84,36,252,12,84,36,252,36,
%U 252,108,756,12,84,36,252,36,252,108,756,36,252,108,756,108,756,324
%N First differences of A160118.
%C Number of cells turned "ON" at n-th stage of the cellular automaton of A160118.
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>.
%e From _Omar E. Pol_, Mar 21 2011: (Start)
%e If written as a triangle begins:
%e 1,
%e 8,
%e 4,28,
%e 4,28,12,84,
%e 4,28,12,84,12,84,36,252,
%e 4,28,12,84,12,84,36,252,12,84,36,252,36,252,108,756,
%e (End)
%t With[{d = 2}, wt[n_] := DigitCount[n, 2, 1]; f[n_] := 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}]]; f[0] = 0; f[1] = 1; Differences[Array[f, 100, 0]]] (* _Amiram Eldar_, Feb 02 2024 *)
%Y Cf. A139251, A160118, A160411, A160413, A160417.
%K nonn
%O 1,2
%A _Omar E. Pol_, Jun 13 2009
%E More terms (a(8)-a(38)) from _Nathaniel Johnston_, Nov 14 2010
%E 21 terms corrected between a(13) and a(38), and more terms (a(39)-a(48)) from _Omar E. Pol_, Mar 21 2011
%E More terms from _Amiram Eldar_, Feb 02 2024
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