%I #19 Feb 24 2021 02:48:19
%S 0,1,4,8,14,20,26,34,46,56,62,70,82,94,106,122,146,164,170,178,190,
%T 202,214,230,254,274,286,302,326,350,374,406,454,488,494,502,514,526,
%U 538,554,578,598,610,626,650,674,698,730,778,814,826,842,866,890,914,946
%N Zero together with the partial sums of A105321.
%H Shawn A. Broyles, <a href="/A173522/b173522.txt">Table of n, a(n) for n = 0..10000</a>
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
%H T. Pisanski and T. W. Tucker, <a href="http://www.imfm.si/preprinti/PDF/00696.pdf">Growth in Repeated Truncations of Maps</a>, Preprint series, Univ. of Ljubljana, Vol. 38 (2000), 696.
%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>
%t f[n_] := f[n] = Sum[ Binomial[1, n - k]Mod[ Binomial[k, j], 2], {k, 0, n}, {j, 0, k}]; g[n_] := Sum[ f@k, {k, 0, n}]; Array[g, 55, 0] (* _Robert G. Wilson v_, Jun 28 2010 *)
%o (PARI) f(n) = sum(k=0, n, binomial(1, n-k)*sum(j=0, k, binomial(k, j) % 2));
%o a(n) = if (n==0, 0, sum(k=0, n-1, f(k))); \\ or
%o lista(nn) = {print1(s=0, ", "); for (n=0, nn-1, s += f(n); print1(s, ", "););} \\ _Michel Marcus_, Apr 29 2018
%Y Cf. A105321, A139250, A173537.
%K nonn
%O 0,3
%A _Omar E. Pol_, May 29 2010
%E More terms from _Robert G. Wilson v_, Jun 28 2010