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

0,3

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

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 *)

Prog

(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

Crossrefs

Cf. A105321, A139250, A173537.

Sequence in context: A176949 A274968 A317109 * A049420 A232996 A317292

Adjacent sequences: A173519 A173520 A173521 * A173523 A173524 A173525

Keyword

nonn

Author

Omar E. Pol, May 29 2010

Extensions

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

Status

approved