A266510 Partial sums of A266509.

0, 0, 1, 2, 3, 4, 7, 10, 11, 12, 15, 18, 23, 28, 35, 42, 43, 44, 47, 50, 55, 60, 67, 74, 79, 84, 95, 106, 123, 140, 155, 170, 171, 172, 175, 178, 183, 188, 195, 202, 207, 212, 223, 234, 251, 268, 283, 298, 303, 308, 319, 330, 347, 364, 387, 410, 439, 468, 503, 538, 579, 620, 651, 682, 683, 684, 687, 690, 695, 700

Offset: 1

Author

Omar E. Pol, Dec 30 2015

Keywords

• nonn

Comments

Also A256265 and twice the terms of A256264 interleaved, with a(1) = 0.

It appears that this sequence has a fractal (or fractal-like) behavior.

First differs from A266530 at a(55), with which it shares infinitely many terms.

First differs from A266540 at a(25), with which it shares infinitely many terms.

For an illustration of initial terms consider the diagram of A256264 in the fourth quadrant of the square grid together with a reflected copy in the second quadrant.

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A256263, A256264, A256265, A266509, A266530, A266540.

Programs

Mathematica

Accumulate@Riffle[#, #] &@ Flatten@Join[{0}, NestList[Join[#, Range[ Length[ #] - 1]*6 - 1, {2 #[[-1]] + 1}] &, {1}, 5]] (* Ivan Neretin, Feb 14 2017 *)

Formula

a(2n-1) = A256265(n).

a(2n) = 2 * A256264(n-1).

a(n) = (a(n-1) + a(n+1))/2, if n is an odd number greater than 1.