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

Author

Gary W. Adamson, May 24 2009

Keywords

• nonn

Examples

			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).
		

Links

• 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. A139251, A160552, A139250, A001045

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,...).