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A151553 G.f.: (1 + x) * Prod_{ n >= 1} (1 + x^(2^n-1) + x^(2^n)). 5
1, 2, 2, 2, 3, 4, 3, 2, 3, 4, 4, 5, 7, 7, 4, 2, 3, 4, 4, 5, 7, 7, 5, 5, 7, 8, 9, 12, 14, 11, 5, 2, 3, 4, 4, 5, 7, 7, 5, 5, 7, 8, 9, 12, 14, 11, 6, 5, 7, 8, 9, 12, 14, 12, 10, 12, 15, 17, 21, 26, 25, 16, 6, 2, 3, 4, 4, 5, 7, 7, 5, 5, 7, 8, 9, 12, 14, 11, 6, 5, 7, 8, 9, 12, 14, 12, 10, 12, 15, 17, 21, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..16383

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

Recurrence: a(0)=1, a(1) = a(2) = 2; a(2^m-1)=2 for m >= 2; a(2^m) = 3 for m >= 2; a(2^m-2) = m for m >= 3; otherwise, for m >= 5, if m=2^i+j (0 <= j < 2^i - 1), a(m) = a(j) + a(j+1).

a(n) = sum_{k >= 0, n+k odd} binomial(A000120(n+k),k); the sum may be restricted further to k <= 2*A000523(n+1) [based on Hagen von Eitzen's formula for A151552].

EXAMPLE

If formatted as a triangle:

.1,

.2,

.2,2,

.3,4,3,2,

.3,4,4,5,7,7,4,2,

.3,4,4,5,7,7,5,5,7,8,9,12,14,11,5,2,

.3,4,4,5,7,7,5,5,7,8,9,12,14,11,6,5,7,8,9,12,14,12,10,12,15,17,21,26,25,16,6,2,

.3,4,4,5,7,7,5,5,7,8,9,12,14,11,6,5,7,8,9,12,14,12,10,12,15,17,21,26,25,16,7

... 5,7,8,9,12,14,12,10,12,15,17,21,26,25,17,11,12,15,17,21,26,26,22,22,27,32,38,47,51,41,22,7,2,

.3,4,4,5,7,7,4,2, ...

CROSSREFS

Cf. A139250, A151550, A151551, A151552.

Sequence in context: A286614 A023508 * A151714 A039644 A281945 A163107

Adjacent sequences:  A151550 A151551 A151552 * A151554 A151555 A151556

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, May 20 2009

STATUS

approved

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)