A266510 - OEIS

%I #46 Feb 22 2023 21:42:31

%S 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,

%T 84,95,106,123,140,155,170,171,172,175,178,183,188,195,202,207,212,

%U 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

%N Partial sums of A266509.

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

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

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

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

%C 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.

%H Ivan Neretin, <a href="/A266510/b266510.txt">Table of n, a(n) for n = 1..8192</a>

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

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

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

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

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

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

%K nonn

%O 1,4

%A _Omar E. Pol_, Dec 30 2015