A163267 Partial sums of A118977.

0, 1, 2, 4, 5, 7, 10, 13, 14, 16, 19, 22, 25, 30, 36, 40, 41, 43, 46, 49, 52, 57, 63, 67, 70, 75, 81, 87, 95, 106, 116, 121, 122, 124, 127, 130, 133, 138, 144, 148, 151, 156, 162, 168, 176, 187, 197, 202, 205, 210, 216, 222, 230, 241, 251, 258, 266, 277, 289, 303, 322, 343, 358

Offset: 0

Author

Gary W. Adamson, Jul 24 2009

Keywords

• nonn

Comments

Can be considered toothpick sequence for N=1.

Based on a consistent set of rules for generating toothpick sequences.

Cf. A139250 where (1, 1, 3, 1, 3, 5, 7, ...) is convolved with (1, 2, 2, 2, ...) and A162958 where A162956 is convolved with (1, 3, 3, 3, ...); the present sequence can be considered toothpick N=1 since A118977 is convolved with (1, 1, 1, ...).

Arranged in array fashion, the first three toothpick sequences would be:

N=1: A163267: (1, 2, 4, 5, 7, 10, 13, 14, ...)

N=2: A139250: (1, 3, 7, 11, 15, 23, 35, 43, ...)

N=3: A162958: (1, 4, 10, 19, 25, 40, 67, 94, ...)

...

Is there an illustration of this sequence using toothpicks? - Omar E. Pol, Dec 13 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• 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.]
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A118977, A139250, A162958.

Programs

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = (j = n - 2^Floor[Log[2, n]]; a[j] + a[j + 1]); Table[Sum[a[n], {n, 0, k}], {k, 0, 20}] (* G. C. Greubel, Dec 12 2016 *)

Extensions

Edited and extended by N. J. A. Sloane, Jan 07 2010