A160704 Jacobsthal sequence A001045 convolved with A139251 (first differences of toothpick numbers).

1, 3, 9, 19, 41, 87, 181, 363, 729, 1463, 2933, 5871, 11753, 23523, 47061, 94123, 188249, 376503, 753013, 1506031, 3012073

Offset

1,2

Links

Table of n, a(n) for n=1..21.

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

Formula

a(n) = 2*a(n-1) + A160552, where A160552 begins with offset 1: (1, 1, 3, 1, 3, 5, 7, 1, 3, 5, 7, 5,...).

Example

a(4) = 19 = (1, 1, 3, 5) dot (4, 4, 2, 1) = (4 + 4 + 6 + 5).
a(4) = 19 = 2*9 + 1, where "1" = A160552(4), A160552 = (1, 1, 3, 1, 3, 5, 7,...)
Using the latter method, we create a heading = row 1:
1,...1,...3,...1,....3,...5,....7,....1,....3,.....5, = A160552 with offset 1.
1...3,....9,...19,..41,..87,..181,..363,..729,..1463,...
...such that a(n) = 2*a(n-1) = term above a(n), or a(n) = 2*a(n-1) + A160552(n). Example: a(6) = 87 = 2*41 + 5, where 5 = A160552(6).

Crossrefs

Cf. A139251, A160552, A139250, A001045

Sequence in context: A307541 A268403 A241626 * A279673 A146662 A145947

Adjacent sequences: A160701 A160702 A160703 * A160705 A160706 A160707

Keyword

nonn

Author

Gary W. Adamson, May 24 2009

Status

approved