A160415 First differences of A160118.

1, 8, 4, 28, 4, 28, 12, 84, 4, 28, 12, 84, 12, 84, 36, 252, 4, 28, 12, 84, 12, 84, 36, 252, 12, 84, 36, 252, 36, 252, 108, 756, 4, 28, 12, 84, 12, 84, 36, 252, 12, 84, 36, 252, 36, 252, 108, 756, 12, 84, 36, 252, 36, 252, 108, 756, 36, 252, 108, 756, 108, 756, 324

Offset

1,2

Comments

Number of cells turned "ON" at n-th stage of the cellular automaton of A160118.

Links

Table of n, a(n) for n=1..63.

Index entries for sequences related to cellular automata.

Example

From Omar E. Pol, Mar 21 2011: (Start)
If written as a triangle begins:
1,
8,
4,28,
4,28,12,84,
4,28,12,84,12,84,36,252,
4,28,12,84,12,84,36,252,12,84,36,252,36,252,108,756,
(End)

Mathematica

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 *)

Crossrefs

Cf. A139251, A160118, A160411, A160413, A160417.

Sequence in context: A307266 A173855 A143368 * A160411 A033473 A238163

Adjacent sequences: A160412 A160413 A160414 * A160416 A160417 A160418

Keyword

nonn

Author

Omar E. Pol, Jun 13 2009

Extensions

More terms (a(8)-a(38)) from Nathaniel Johnston, Nov 14 2010

21 terms corrected between a(13) and a(38), and more terms (a(39)-a(48)) from Omar E. Pol, Mar 21 2011

More terms from Amiram Eldar, Feb 02 2024

Status

approved