A266535 Sums of two successive terms of A256249, with a(0) = 0.

0, 1, 3, 7, 11, 15, 23, 35, 43, 47, 55, 67, 83, 103, 127, 155, 171, 175, 183, 195, 211, 231, 255, 283, 315, 351, 391, 435, 483, 535, 591, 651, 683, 687, 695, 707, 723, 743, 767, 795, 827, 863, 903, 947, 995, 1047, 1103, 1163, 1227, 1295, 1367, 1443, 1523, 1607, 1695, 1787, 1883, 1983, 2087, 2195, 2307, 2423, 2543, 2667, 2731

Offset: 0

Author

Omar E. Pol, Jan 02 2016

Keywords

• nonn

Comments

Also bisection of A266540.

It appears that this sequence has a fractal-like behavior (see Plot 2, A139250 vs. this sequence).

First differs from both the toothpick sequence A139250 and A256265 at a(12), with which it shares infinitely many terms.

Links

• Michel Marcus, 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

Crossrefs

Cf. A006257, A139250, A256249, A256265, A266539, A266540.

Programs

Mathematica

Most@ # + Rest@ # &@ Accumulate@ Join[{0, 0}, Flatten@ Table[Range[1, 2^n - 1, 2], {n, 0, 6}]] (* Michael De Vlieger, Jan 05 2016, after Ivan N. Ianakiev at A256249 *)

PARI

f(n)=n++; b=#binary(n>>1); (4^b-1)/3+(n-2^b)^2; \\ A256249
a(n) = if (n, f(n)+f(n-1), 0);