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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) adjacent to a(n-1)} a(i). 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, etc.

Thus:

12----20----34

/ \

/ \

7 1-----1 55

\ / /

\ / /

638 4-----2 90

\ /

\ /

394---240---148

CROSSREFS

Cf. A094926, A078510, A079421, A079422.

Sequence in context: A005182 A329397 A172524 * A289168 A340217 A289000

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 January 29 23:01 EST 2023. Contains 359939 sequences. (Running on oeis4.)