A256531 - OEIS

%I #54 Nov 15 2023 15:06:11

%S 0,1,8,12,28,12,36,60,68,12,36,60,84,108,132,156,148,12,36,60,84,108,

%T 132,156,180,204,228,252,276,300,324,348,308,12,36,60,84,108,132,156,

%U 180,204,228,252,276,300,324,348,372,396,420,444,468,492,516,540,564,588,612,636,660,684,708,732,628,12,36,60,84,108

%N First differences of A256530.

%C Number of cells turned ON at n-th stage of cellular automaton of A256530.

%C Similar to A261695 which shares infinitely many terms.

%H Paolo Xausa, <a href="/A256531/b256531.txt">Table of n, a(n) for n = 0..8191</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>

%e With the positive terms written as an irregular triangle in which the row lengths are the terms of A011782 the sequence begins:

%e 1;

%e 8;

%e 12, 28;

%e 12, 36, 60, 68;

%e 12, 36, 60, 84, 108, 132, 156, 148;

%e 12, 36, 60, 84, 108, 132, 156, 180, 204, 228, 252, 276, 300, 324, 348, 308;

%e ...

%e The terms of the rows that start with 12 are also the initial terms of A073762, except the last term of every row, hence rows converge to A073762.

%t With[{z=7},Differences[Join[{0,0},Flatten[Array[(2^#-1)^2+12Range[0,2^(#-1)-1]^2&,z]]]]] (* Generates 2^z terms *) (* _Paolo Xausa_, Nov 15 2023, after _Omar E. Pol_ *)

%o (GW-BASIC) 10' a256531 First 2^z-1 positive terms: 20 z=6: defdbl a: for i=1 to z: for j=0 to 2^(i-1)-1: n=n+1: a(n)=(2^i-1)^2 + 3*(2*j)^2: print a(n)-a(n-1);: next j: next i: end

%Y Cf. A011782, A073762, A139251, A147582, A161411, A161415, A256530, A261695.

%K nonn,tabf

%O 0,3

%A _Omar E. Pol_, Apr 21 2015