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A094925 A hexagonal spiral Fibonacci sequence. 2
1, 1, 2, 4, 7, 12, 20, 34, 55, 90, 148, 240, 394, 638, 1043, 1688, 2750, 4450, 7232, 11736, 19002, 30827, 49884, 80856, 130978, 211982, 343348, 555964, 899706, 1456702, 2358089, 3815834, 6176654, 9996926, 16176330, 26180456, 42368468, 68567892 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Consider the following spiral:

......a(6)..a(7)..a(8)

...a(5)..a(1)..a(2)..a(9)

a(14).a(4)..a(3)..a(10)

...a(13).a(12).a(11)

Then a(1)=1, a(n)=a(n-1)+Sum{a(i) : a(i) adjacent to a(n-1)}. Here 6 terms around a(m) touch a(m).

LINKS

Manfred Scheucher, Table of n, a(n) for n = 1..1323

N. Fernandez, Spiro-Fibonacci numbers

Manfred Scheucher, Sage Script

FORMULA

a(n) ~ c*phi^n with phi=1.61803... being the golden ratio and c = 0.78529667298898361017570049509486675274402985275383398273772345738007479334754... (conjectured). Cf. A094926. - Manfred Scheucher, Jun 03 2015

EXAMPLE

a(2) = a(1) = 1

a(3) = a(1)+a(2) = 2

a(4) = a(1)+a(2)+a(3) = 4

a(5) = a(1)+a(3)+a(4) = 7

a(6) = a(1)+a(4)+a(5) = 12

a(7) = a(1)+a(5)+a(6) = 20

thus:

......12....20...34

...7.....1.....1.....55

638...4.....2.....90

..394....240..148

CROSSREFS

Cf. A094926, A078510, A079421, A079422.

Sequence in context: A093607 A005182 A172524 * A289168 A289000 A289028

Adjacent sequences:  A094922 A094923 A094924 * A094926 A094927 A094928

KEYWORD

nonn,easy

AUTHOR

Yasutoshi Kohmoto

EXTENSIONS

a(15) - a(38) from Nathaniel Johnston, Apr 26 2011

STATUS

approved

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Last modified April 20 08:49 EDT 2019. Contains 322306 sequences. (Running on oeis4.)