A256251 First differences of A256250.

1, 4, 4, 12, 4, 12, 20, 28, 4, 12, 20, 28, 36, 44, 52, 60, 4, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 4, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 4, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100

Offset: 0

Author

Omar E. Pol, Mar 20 2015

Keywords

• nonn
• tabf

Comments

Number of cells turned ON at n-th stage in the structure of A256250.

Apart from the initial 1, four times A006257 (Josephus problem).

Examples

			Written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
4;
4,12;
4,12,20,28;
4,12,20,28,36,44,52,60;
4,12,20,28,36,44,52,60,68,76,84,92,100,108,116,124;
4,12,20,28,36,44,52,60,68,76,84,92,100,108,116,124,132,140,148,156,164,172,180,188,196,204,212,220,228,236,244,252;
...
Row sums give A000302.
Right border gives A173033.
		

Links

• Danny Rorabaugh, Table of n, a(n) for n = 0..10000
• 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 sequences related to the Josephus Problem

Crossrefs

Cf. A000302, A006257, A011782, A028399, A139251, A147582, A162793, A169708, A256239.

Programs

PARI

a(n) = if(n, 8*(n - 2^logint(n,2)) + 4, 1)

Sage

[1] + [8*(n - 2^floor(log(n,base=2))) + 4 for n in range(1,77)] # Danny Rorabaugh, Apr 20 2015

Formula

a(0) = 1. For n >= 1; a(n) = 4*A006257(n).

For n>0, a(n) = 8*(n - 2^floor(log_2(n))) + 4 (by the formula of Gregory Pat Scandalis in A006257). - Danny Rorabaugh, Apr 20 2015