A173522 Zero together with the partial sums of A105321.

0, 1, 4, 8, 14, 20, 26, 34, 46, 56, 62, 70, 82, 94, 106, 122, 146, 164, 170, 178, 190, 202, 214, 230, 254, 274, 286, 302, 326, 350, 374, 406, 454, 488, 494, 502, 514, 526, 538, 554, 578, 598, 610, 626, 650, 674, 698, 730, 778, 814, 826, 842, 866, 890, 914, 946

Offset: 0

Author

Omar E. Pol, May 29 2010

Keywords

• nonn

Links

• Shawn A. Broyles, Table of n, a(n) for n = 0..10000
• David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, 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.]
• T. Pisanski and T. W. Tucker, Growth in Repeated Truncations of Maps, Preprint series, Univ. of Ljubljana, Vol. 38 (2000), 696.
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A105321, A139250, A173537.

Programs

Mathematica

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 *)

PARI

f(n) = sum(k=0, n, binomial(1, n-k)*sum(j=0, k, binomial(k, j) % 2));
a(n) = if (n==0, 0, sum(k=0, n-1, f(k))); \\ or
lista(nn) = {print1(s=0, ", "); for (n=0, nn-1, s += f(n); print1(s, ", "););} \\ Michel Marcus, Apr 29 2018

Extensions

More terms from Robert G. Wilson v, Jun 28 2010