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A160704 Jacobsthal sequence A001045 convolved with A139251 (first differences of toothpick numbers). 1
1, 3, 9, 19, 41, 87, 181, 363, 729, 1463, 2933, 5871, 11753, 23523, 47061, 94123, 188249, 376503, 753013, 1506031, 3012073 (list; graph; refs; listen; history; text; internal format)
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: A208972 A268403 A241626 * A279673 A146662 A145947

Adjacent sequences:  A160701 A160702 A160703 * A160705 A160706 A160707

KEYWORD

nonn

AUTHOR

Gary W. Adamson, May 24 2009

STATUS

approved

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Last modified January 21 11:00 EST 2019. Contains 319351 sequences. (Running on oeis4.)