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A187211 First differences of A187210. 9
0, 1, 4, 7, 12, 22, 20, 22, 40, 54, 40, 22, 40, 54, 56, 70, 120, 134, 72, 22, 40, 54, 56, 70, 120, 134, 88, 70, 120, 150, 168, 246, 360, 326, 136, 22, 40, 54, 56, 70, 120, 134, 88, 70, 120, 150, 168, 246, 360, 326, 152, 70, 120, 150, 168, 246, 360, 342, 232, 246, 376, 454, 568, 838, 1032 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of Q-toothpicks added at n-th stage to the Q-toothpick structure of A187210.

For the connection with A139251, the first differences of the toothpick sequence A139250, see the Formula section. - Omar E. Pol, Apr 02 2016

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..177

David Applegate, The movie version

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

Nathaniel Johnston, C script

Nathaniel Johnston, The Q-Toothpick Cellular Automaton

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

FORMULA

a(2^n + 2) = 16 + 8(2^(n-1) - 1), n >= 3. [Nathaniel Johnston, Mar 26 2011]

From Omar E. Pol, Apr 02 2016: (Start)

a(n) = floor(sqrt(2*n^3)), if 0<=n<=2 or n=6.

a(n) = 2*A139251(n-2) + A267699(n-2) + A267695(n-1), if 3<=n<=5 or n>=7.

(End)

EXAMPLE

Written as an irregular triangle the sequence begins:

0;

1;

4;

7;

12;

22, 20;

22, 40, 54, 40;

22, 40, 54, 56, 70, 120, 134, 72;

22, 40, 54, 56, 70, 120, 134, 88, 70, 120, 150, 168, 246, 360, 326, 136;

...

The rows of this triangle tend to A188156.

From Omar E. Pol, Apr 02 2016: (Start)

For n = 5 we have that A139251(5-2) = 4, A267699(5-2) = 7 and A267695(5-1) = 7, so a(5) = 2*4 + 7 + 7 = 22.

For n = 10 we have that A139251(10-2) = 8, A267699(10-2) = 20 and A267695(10-1) = 4, so a(10) = 2*8 + 20 + 4 = 40.

(End)

Starting from a(3) = 7 the row lengths of triangle are the terms of A011782. - Omar E. Pol, Apr 04 2016

CROSSREFS

Cf. A011782, A139250, A139251, A172472, A182841, A187210, A187221, A267695, A267699.

Sequence in context: A117949 A228879 A010901 * A023624 A123194 A208668

Adjacent sequences:  A187208 A187209 A187210 * A187212 A187213 A187214

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Mar 07 2011

EXTENSIONS

Terms after a(7) from Nathaniel Johnston, Mar 26 2011

STATUS

approved

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Last modified May 23 16:25 EDT 2017. Contains 286925 sequences.